Consequence Analysis and Modelling

193

11.5.

CONSEQUENCE

ANALYSIS

AND MODELLING

Michalis D. Christou

In this section the consequences of major accidents are discussed. The nature of these consequences, the relevance of the topic given by the 'Seveso Directive', and methods used for their modelling and assessment are presented. The steps and structure of the consequence assessment procedure are given and the various models for source-term definition, dispersion, fire and explosion and dose/effect (vulnerability) modelling are described. The presentation of the models is mainly focused on the description of the physical phenomena taking place, the principles of the mathematical models available, the input and output variables, and the relation with other models. Next, combining various models and obtaining meaningful risk measures from the integration of the individual results is discussed. Finally, the nature and origin of uncertainties in the consequence assessment procedure are described and possible ways to handle these uncertainties are mentioned.

1.

INTRODUCTION

Together with the quantification of the "likelihood" of accident occurrences (treated in the subsequent Section II.6), the assessment of the consequences of such events is a significant step in the quantification of risk. By this, the undesirable consequences of an accident are estimated and quantitatively evaluated. Consequence assessment and modelling is based on models for source-term definition, dispersion calculations, fire and explosion models, and finally vulnerability models for the estimation of health effects. The purpose of this section is mainly to introduce the models and the basic philosophy of consequence assessment. It provides an outline of the available models and focuses mainly on their rationale and practical use. The purpose of this section is not the explicit and detailed description of the models used for consequence assessment nor the attempt of an exhaustive listing of all available models. For these latter purposes one should refer to the literature for more information. Here, the objective is to show how the various models are put together in order to provide estimations of the consequences of the potential accidents.

2.

NATURE OF THE CONSEQUENCES OF MAJOR ACCIDENTS

According to the definition followed by most risk experts and adopted by the 'Seveso II Directive', risk is a combination of the magnitude of undesirable consequences and the "likelihood" of these consequences occurring. As already mentioned in Section II.2. the terms "risk" and "undesirable consequence" are so much related that risk cannot be thought of without considering the relevant undesirable consequences.

194 Trying to classify the consequences of major accidents, three main groups can be identified: 9 9 9

consequences to human beings, consequences to the environment, socio-economic consequences.

The first category is naturally the main concern in major accidents. It concerns the adverse effects of the accidents to the employees and the population around the establishment. These effects can further be divided into acute and latent effects, into fatalities and injuries, and into various types of injury (e.g. bums of various degrees, breathing problems, etc.). The second category concerns the effects of an accident to the environment and to the ecosystem (e.g. accidental pollution of the surface water or ground water, destruction of the flora and/or fauna around a site, etc.). Further distinction can be made in accidental pollution of soil, surfacewater, ground-water and air, adverse effects to the species constituting the flora and fauna of the site, and finally damage of the ecosystem. The third category includes the economic losses of the owner company and the damages to constructions caused by the accident (e.g. loss of production, raw material, equipment, damages to buildings, etc.). Although the consequences of major accidents are extended to many receptors and cover several different types of effects, the main focus is usually given to the effects to human beings. The same rule has also been followed in this section: Focus has been given to the methods and models for the assessment of the impact to human health, mainly concerning fatality and sometimes injury. However, this does not imply that there is a lack of models for the assessment of environmental or economic damage, or that such an assessment is useless and is never being performed. There is a variety of human health effects studied in the assessment of major accident consequences: the toxicological effects from the inhalation and exposure to toxic substances (direct and indirect exposure through various routes), the thermal radiation effects (bums), caused by the thermal radiation during the burning of the flammable substances, the pressure wave effects, caused by the overpressure waves during the explosion of flammable substances or explosive materials or dusts, the projectiles, i.e. mechanical particles which are projected like missiles during an explosion, the effects of carcinogenic substances, the exposure to which can cause cancers and tumours.

D

CONSEQUENCE ASSESSMENT IN THE CONTEXT OF THE 'SEVESO II DIRECTIVE'

The concern about the consequences of major accidents is spread throughout the 'Seveso II Directive'. In Article 1, the Directive's aim is defined as:

195 "the prevention of major accidents which involve dangerous substances, and the limitation of their consequences for man and the environment." According to Article 9, paragraph 1(b), one of the purposes of the Safety Report produced by the operator is to demonstrate that "... the necessary measures have been taken to prevent such accidents and to limit their consequences for man and the environment." Moreover, as specified in Annex II, item IV.B, the "assessment of the extent and severity of the consequences of identified major accidents" is considered among the minimum data and information to be included in the Safety Report. These quotations of articles of the Directive indicate the importance given by the main European legislative instrument for the control of major accident hazards to the consequences of the accidents and, hence, to the assessment of these consequences. Moreover, consequence assessment is part of the evaluation of the proper design and the adequacy of the protective measures in the plant, and is input to the decision making process in many risk-related decisions (e.g. land use planning).

4.

THE STRUCTURE OF CONSEQUENCE ASSESSMENT

The consequence assessment is an essential part of any attempt for quantification of risk, of any attempt for risk assessment. As discussed in detail in Section III.1 risk assessment, in its broader definition, is a structured procedure that evaluates and compares the level of risk imposed by hazard sources identified within or external to the installation. In general, the procedure tries to answer to four important questions regarding the installation: what can go wrong? how will the installation's safety systems react to these events? how "likely" is this to happen? what will be the consequences should the safety systems fail? The first step of this procedure consists of the systematic identification of the initiating events that can lead to an accident. Next, the reaction of the safety systems and safety precautions of the installation to these events is analysed and the "likelihood" of the combined event sequences resulting in a possible accident is estimated together with the extent of the consequences of the possible accident. Eventually, all these estimates are integrated into final risk measures (see Section 111.1). After having identified the possible "initiating events" and having analysed the reactions of the installation's safety measures to these events together with "likelihood" estimations, the procedure results in a number of possible plant damage states that have to be taken into account (probabilistic cut-off criteria are often applied to select "realistic" damage states). These states contain all the necessary information about the plant so that the consequences of the potential accidents can be quantified.

196 The condition - or the damage state - of the plant is not the only parameter on which the consequences of an accident depend. Meteorological conditions, population data, the topography of the site and the plant's environment are also necessary parameters for the estimation of the consequences. Since the number of possible combinations of all these parameters is enormous, a classification procedure is required. Combinations that lead to similar consequences are grouped together and constitute the release categories.

A release category is therefore determined by the values of the parameters determining the plant damage state and representative values of meteorological and other (population, topography, etc.) data. The consequences of this combination of data, which represents the whole category, are further calculated and a frequency / probability is assigned to these results, which corresponds to the whole category. In order to calculate the consequences to man and the environment the consequence assessment procedure simulates the evolution of an accident and follows the physical phenomena involved. The normal evolution of an accident is, as follows: Initially, there is a release of the hazardous substance to the environment. This release can be in gaseous form, in liquid form or a two-phase flow. If the substance is in liquid form, then this liquid will be evaporated. If the substance is flammable, there is the possibility of immediate ignition. If the substance is toxic, or if it is flammable but not ignited immediately, then the gaseous form will be dispersed in the atmosphere. The toxic substance might be inhaled by people. If the dose exceeds certain thresholds, there is the possibility of injuries or even fatalities. The flammable substance might be ignited. The persons nearby will suffer from the thermal and overpressure effects of the fire and/or explosion. If a flammable substance is released in liquid form, then a pool will be formed. If in addition there is an ignition source available, this will result in a pool fire. In order to assess the consequences of the accident, the analyst has to model all the above phenomena. Models have to be developed and be available for all the phenomena. Therefore, the analyst simulates the progress of the accident by using the adequate combinations of models. More specifically, the analyst uses a set of models for the the the the the

definition of source-terms, dispersion modelling, modelling of fires, modelling of explosions, estimation of the vulnerability of the receptors.

The following Figure 11.5.1 shows the schematic structure of consequence assessment models.

197

Figure 11.5.1: The Structure of Consequence Assessment Models

WEATHER CONDITIONS ~ OUTFLOW RATE

VAPOUR

,,.._I DISPERSION I "-I MODEL

I.,~176176 L~ EVAPORATION~_ |

t

TOPOGRAPHY

RATE

MODEL

EXPOSURE (DOSE) ASSESSMENT

CONSEQUENCE ASSESSMENT

EMERGENCY RESPONSE PLAN

VULNERABILITY MODEL

In the following subsections, a brief description of these models will be given. Since the presentation of the topics is not based on any specific set of models and computer codes, the description will be generic, giving mainly the description of the phenomena, the usual input and output of the models, their purpose and their position in the overall structure of consequence assessment. It should also be noted that the models and the corresponding phenomena described here are the most common ones. There is a plethora of phenomena appearing in certain cases, for which models are available, too (e.g. roll-over). For a description of these models and phenomena, the reader should refer to the relevant literature.

5.

SOURCE-TERM MODELS

5.1

Description of the Phenomena

The first step in the assessment of consequences is the definition of source-terms. This means the determination of the quantity and the conditions of the released substance. Since most of the hazardous incidents start with a discharge of the flammable or toxic material from its normal containment (tank, vessel, piping), the evaluation of the source-terms is very important for the next steps of the consequence assessment. An important parameter that regulates the sequence of phenomena is the duration of the release. If the duration is very small, the release can be considered as instantaneous, or quasiinstantaneous. On the other hand, if the duration is large compared to the overall time-scale of the accident, then the release is assumed as continuous and is modelled accordingly. For practical reasons, most analysts consider as instantaneous a release with duration less than 3-5 minutes. As mentioned above, the released quantity might be in the liquid or gaseous phase, or a twophase flow might occur. If there is liquid involved, it usually forms a pool and starts evaporating. For carrying out this evaporation, the substance has to absorb heat from its

198 environment (air, soil, droplets, liquid phase). The vapours of the substance will be added to the gaseous phase, resulting in an increase of the quantity to be dispersed.

5.2

Models

Discharge models: The models for liquid and gas discharge are well-known in engineering (e.g. the Bernoulli equation). The adequate model to be selected depends on the phase (i.e. whether or not the release is in liquid / gaseous / two-phase form) and the conditions of the released substance. A typical simple example of discharge model is the Bernoulli equation, which applies to liquid discharge:

mL = Ca "A ' d ' I 2 (~P -+d 2po) g H where:

J~/L Ca A d P Pa

g H

is is is is is is is is

the the the the the the the the

(1)

liquid mass discharge rate (kg/s) discharge coefficient orifice area (m 2) liquid density (kg/m 3) absolute storage pressure (N/m 2) absolute ambient pressure (N/m 2) acceleration of a mass due to gravity (rn/s 2) height of liquid above the orifice (m)

For gas outflow, more complicated models should be applied, and distinction should be made on whether the outflow is sonic (high pressure) or sub-sonic (low pressure). More details can be found, for example, in references [ 1,8], as well as in any consequence assessment computer code (e.g. the ones described in references [2,4-7]). Another case of gas discharge worth mentioning is the flow from relief valves, i.e. valves specifically designed in order to relief the increased pressure in a vessel and thus prevent its rupture due to overpressure. For a two-phase flashing discharge, empirical equations have been proposed (see, for example, [8, 1]).

Evaporation models: As far as the evaporation of the released substance is concerned, various models are available in the literature and some of them have also been implemented into computer codes. Their behaviour mainly depends on whether the dominant evaporation mechanism is heat transfer (from the soil and air) or the blowing wind. Pool evaporation models are based on fundamental principles of thermodynamics. In the case where the dominant mechanism is heat transfer from the soil and air, the evaporation rate is given from energy equilibrium, i.e.

199 considering that the total heat flux taken from the air and ground will be used in order to heat and evaporate the released substance. More advanced models can take into consideration cases where the pool radius is increasing (no dike available).

5.3

Input - Output

Usually the outflow (or discharge) models take as input the conditions (e.g. pressure, temperature) inside and outside the containment, together with the characteristics of the substance. The size, shape and location of the orifice are also required. These data derive directly from the operation conditions of the installation and the assumptions associated with the accident scenario under consideration. The output of the discharge models is the quantitative determination of the release. This includes the discharge quantity or rate, the duration of the discharge, the conditions of the released substance, i.e. whether it is in liquid, gaseous or flashing (two-phase) phase. The evaporation models usually require the variables calculated by the outflow models and the weather conditions.

5.4

Relation with Other Models

The source-term models require data from the accident scenario description, the details of the installation and the weather conditions. Their output is required for the dispersion calculations.

6.

DISPERSION MODELS

6.1

Description of the Phenomena

After released in the atmosphere, the substance forms a cloud, which is then dispersed downwinds. There are two different mechanisms of dispersion: The buoyant dispersion for gases lighter than air. These clouds are passively transported by the wind; The heavy gas dispersion for gases or mixtures heavier than air. In that case, there is a first "slumping" phase, during which the dominant force is gravity since the cloud is heavier than air. During this phase air enters the cloud, heating and diluting it and thus making it lighter. There is a transition phase and then a passive dispersion phase,

200 since the cloud's density has significantly been decreased and it has now become lighter than air.

6.2

Meteorological Conditions- Topography

In general, meteorological conditions and site topography are important parameters in most steps of the consequence assessment procedure. Especially in dispersion phenomena the role of those two parameters is very important - probably among the most important ones. The meteorological conditions are determined by the wind velocity and direction, the air temperature and humidity, atmospheric pressure and the stability class. The latter is a classification depending on parameters such as windspeed and daytime and night-time cloudiness. It has been proposed by Pasquill and Gifford and it consists of 6 classes, ranging from A (extremely unstable) to F (extremely stable). In general, when the weather is stable (classes F, E) or neutral (class D) the released substances are expected to travel longer distances before the concentration drops to low levels. For that reason, stability classes D and F are usually considered as "bad" weather conditions in the dispersion of dangerous substances. Another parameter worth discussing is the site's topography. Again, this parameter plays an important role for the dispersion of the released substances - and therefore to consequence assessment - since it is possible for physical obstacles or peculiarities to protect certain areas or create big problems to others. As an example, the dispersion of dangerous substances in valleys is very different than on fiat terrain. The topography of a site is usually represented by the altitude at each point. The roughness of the ground is also of great importance. Five roughness categories are usually considered in dispersion modelling, corresponding to flat terrain, cultivated land, land with sparse houses, residential area and urban area (with high buildings, sky-scrapers, etc.).

6.3

Models

There are various dispersion models in the literature. They are distinguished according to: The vapour cloud behaviour. There are models for buoyant (also known as passive or Gaussian) dispersion, and models for heavy gas dispersion. The duration of the release, i.e. whether the release can be considered as instantaneous (puff) or continuous (plume). The complexity of modelling. There are simple, "box" models, and complex terrain 3-D models.

201 The Gaussian model: One of the simplest - and probably most extensively used - models, the Gaussian model, is applied for lighter than air gases, or during the passive dispersion phase in general. It is based on the assumption that the concentration of the dangerous substance is normally (Gauss) distributed on both the horizontal and the vertical axes. For a continuous release from an elevated point source at a height H the concentration at a point (x, y, z) from the source is given by

7h I ~y-~lr --(Z--H) 2 -(Z --I-/-/ )2 1 C(x,y,z)--21'C U~yO"z Lexp 20"y ~Lexp 2(~z + exp 21~z2 -

where:

2

-

(2)

O"y

is the distance from the source (x=downwind, y=crosswind, z=vertical) is the concentration of the substance at point (x,y,z) (kg/m 3) is the release rate (kg/s) is the wind velocity (m/s) is the height of the source from the ground (m) is the horizontal dispersion coefficient (m), depending on the

O"z

distance downwind and the stability class. is the vertical dispersion coefficient (m), depending on the

x,y,z c (x,y,z) m

u

H

distance downwind, the stability class and the roughness.

For an instantaneous release, the concentration at a point (x, y, z) from the source is given by

o

c ( x , y , z ) = (2/17)3/20"xGy~z

where:

M t

E{ix_ ,2 exp

-

2

2~,,

y2}lE

--2

2Gy

exp

2cr~

+ exp

2cr~

(3)

is the amount of substance released (kg) is the time elapsed after release (s)

The Lagrangian model: The Lagrangian model simulates the dispersion of a lighter-than-air gas release by assuming that it consists of a number of particles and by studying their airborne transport in a predetermined wind field.

202 The dense-gas "box" model: This is the simplest model applicable for dense (heavier than air) gas releases. The released cloud is modelled as a cylinder, initially with equal radius and height, consisting of a mixture of the dangerous substance in gaseous form, droplets and air. As this cylinder is transported downwinds, the dominant force is gravity and therefore the cylinder's height decreases and its radius increases. This phase is known as the "slumping phase". As air enters the cloud from the edges and the top, the whole mixture is heated and diluted. There is a certain point during that phase at which the cloud is so much diluted that it behaves as lighter than air, dispersed neutrally by the wind. From this point the Gaussian model can be applied to describe the dispersion of the cloud. Concerning continuous releases, the relevant plume formed is modelled as a sequence of thin rectangular slices, for which the same principles apply.

Computational Fluid Dynamics (CFD): These are the most sophisticated - and therefore most powerful and most complicated dispersion models. They are studying the fluid dynamics of the systems, using high degrees of detail in their analysis. A number of differential equations are solved for all three dimensions and at each time instant, describing in this way the dynamics of the flow. Complex terrain, obstacles strange-shaped borders and flow particularities can be considered without problems. The disadvantage of this family of models is the high degree of complexity used, thus requiring a high degree of expertise by the analyst and also an advanced cost for performing the assessment. It should be stressed that the selection of the adequate model to be applied is not a simple and easy issue and depends on the requirements of the study, the availability of models and the desired accuracy of the results.

6.4

Input - Output

Usually the dispersion models require as input the quantity and the initial characteristics of the release, the weather conditions, the topography of the area and the properties of the substance. The main output is the concentration of the substance at each time and point around the source. The meteorological data probably constitute one of the most important input parameters in dispersion modelling. As discussed above, these data refer to wind velocity, wind direction, stability class, ambient temperature, atmospheric pressure and relative humidity. Topography is usually taken into consideration by the altitude at each point around the plant, and the ground roughness of the area.

203

6.5

Relation with Other Models

The dispersion models require data from the source-term models and the meteorological conditions, and give as an output the profile of concentration, which is required for the dose calculation for toxic substances and for the calculation of the burning or the explosive mass for flammables.

7.

FIRE AND EXPLOSION MODELS

In the case of flammable substances it is very likely for the released substance to be ignited, should an ignition source initiate the fire. There are various types of fires:

7.1

Pool Fires

Mainly occur when the released liquid forms a pool, which is then ignited. For modelling the pool fires, the burning rate for the material of interest is considered, the flame height is calculated, the geometric factor (depending on the position of the receptor relative to the flame) is calculated, and the weather conditions are taken into account. The output of the model is the received thermal flux (in kW/m2).

7.2

Jet Fires

The Jet fires result from pressurised releases of flammable gases or liquids. They are modelled as a cylinder of diameter D and length L (the length of the flame), which are calculated mainly from empirical equations. The received thermal flux is then calculated, taking also into consideration the geometric view factor (determined from the position of the receptor in relation to the flame).

7.3

Boiling Liquid Expanding Vapour Explosion (BLEVE)

This explosion occurs from the sudden release of a large mass of pressurised superheated liquid to the atmosphere. The resulting fireball actually derives from the atmospheric burning of a fuel-air cloud in which the energy is mostly emitted in the form of radiant heat. The fireball rises due to buoyancy forces of the hot gases. The effects of a BLEVE include the thermal radiation and the projectiles, while the resulting overpressure is not important.

204

7.4

Explosion Models

The explosion is a very rapid combustion, so that the expansion of the gases results in a rapidly moving pressure wave. Two different cases are distinguished: the deflagration, where the speed of the pressure wave is lower than the speed of sound (at these conditions), and the detonation, where the speed of the pressure wave is greater than the speed of sound. A well-studied type of explosion is the Unconfined Vapour Cloud Explosion (UVCE). For its evaluation, two methods appear in the literature: the TNT model, which calculates the mass of TNT (trinitrotoluene) equivalent to the flammable material released and estimates the overpressure vs. distance from the relevant TNT curve, and the TNO (Dutch research institute) model, which calculates the characteristic explosion length L0, and from this the overpressure vs. distance. It should be noted that UVCE is usually the effect of a delayed ignition of the released flammable substance. In other words, no ignition source was present when the substance was released and, therefore, the formed cloud continued its dispersion downwinds until an ignition source was found. The calculation of the mass participating in the explosion (flammable mass) requires dispersion modelling and calculation of concentration at each point, since there is an upper and a lower flammability limit (UFL and LFL, respectively) for each substance and only between these two limits the substance can be ignited. This means that only the mass corresponding to the part of the cloud between UFL and LFL will participate in the UVCE calculations 1.

7.5

Fragments Projection

An undesired effect usually following the explosion of tanks and vessels is the projection of fragments of these containments, which can then cause the death or injury of people, damages to buildings and structures, or even the initiation of new events and incidents (domino effect). In general, the number, size, direction and projection distance of these projectiles is very difficult to be predicted and modelled. For this reason, attempts to model the phenomenon are usually based on empirical equations and statistical data from previous accidents (see also

Section 11.6).

although many analysts believe that the mass of flammable material is greater than the above mentioned and the calculations should be extended to cover the part of the cloud corresponding to concentration > 1/2 LFL.

205

7.6

Domino Effect

An important undesirable effect mainly associated with fires, explosions and fragment projections is the "domino" effect. It is possible under certain conditions that the accident which occurred in one unit or plant is expanded also to other "neighbouring" units or plants, creating a "chain" major accident with extended consequences. Thus, especially as far as the flammable substances are concerned, attention should be given not only to health effects but also to the resistance of other machinery (tanks, pumps, pipelines, etc.) to certain thermal radiation levels. Article 8 of the 'Seveso II Directive' requires the Competent Authorities of the Member States to identify groups of establishments where domino effects are possible and to take measures in order to avoid their occurrence and limit their consequences.

8.

VULNERABILITY MODELS

8.1

Description of the Phenomena

The source-term, dispersion, fire and explosion models described above provide an evaluation of the incident outcomes in terms of quantification of the main physical parameters (concentration, thermal radiation, overpressure). The vulnerability or dose/response models on the other hand provide an estimation of the effects of these physical phenomena to the receptors. In other words, the purpose of vulnerability models is the quantification of the response of the receptors to these adverse physical phenomena. Three categories of effects are of interest will be analysed in detail: 9 9 9

toxic gas effects, thermal radiation effects, shock wave overpressure effects.

8.2

Models

Toxic effect models: Toxic effect models are employed to assess the consequences to human health as a result of exposure to toxic gases. For a variety of reasons it is difficult to precisely evaluate the effect of an exposure to toxic materials. The main reasons are the fact that there is a variety of effects (e.g. irritation, asphyxiation, blindness, organ system damage, death), and the fact that there is a high degree of variation in response among individuals in a typical population. In addition, there is a significant lack of data concerning these effects, and experimentation is impossible. The only data usually comes from controlled experiments on laboratory animals and the extrapolation from that data to humans is therefore the only available technique.

206 In the attempt to study and analyse the effect of toxic substances, the following thresholds have been defined: 9

LCs0 : Median Lethal Concentration is the concentration of the substance that is expected to cause death within a fixed period in 50% of animals exposed for a specified time (usually 10 min or 30 min);

9

LDs0 : Median Lethal Dose is the dose that is expected to cause death within a fixed period in 50% of animals exposed;

9

IDLH : Immediately Dangerous for Life and Health is the maximum airborne concentration of the substance at which a healthy worker can be exposed for as long as 30 min and still be able to escape without loss of life or other irreversible damage.

Another method to cope with the toxic effects of the substances is the use of Probit function. This method is based on the statistical analysis of the effect to a population of animals (results duly extrapolated to human beings). First, it is acknowledged that the damage caused to a population from the same exposure to the same substance significantly varies, depending on the strength, the health condition and the characteristics of the individuals. For this reason, the concept of toxic dose is determined:

D= foCn(t)dt

(4)

From this toxic dose, the Probit (probability unit) function is calculated, as shown in the following Figure 11.5.2, and the risk (defined as the probability of fatality) is subsequently calculated as

R=O.5• where erf is the error function and P is the probit value.

(5)

207

Figure 11.5.2: The Form of Probit Function for Toxic Exposure, Thermal Radiation and Shock Wave Overpressure 9 Toxic substances Pr obit = a + b In(D) T

where

D = I c" (t)dt

9 F l a m m a b l e s - T h e r m a l radiation Pr obit = - 1 4 . 9 + 2.56 In(D)

where

D=

i 1413 (t)dt 104

0 Pressure wave Pr obit = - I 8.1 + 2.79 In (Ap')

Thermal Radiation Models: As far as the effects of thermal radiation to people and structures are concerned, the following Table 11.5.1 summarises the most important thresholds.

Table 11.5.1" Effects of Thermal Radiation on People and Structures Radiation intensity (kW/m2)

. . . . . O[~served effect

37.5 25 12.5 9.5 4 1.6

,,.

Sufficient to cause damage to process equipmeni . . . . . . . . . . Minimum energy required to ignite wood Minimum energy required for piloted ignition of wood; melting of plastic tubing Pain threshold reached after 8 s; 2nd degree burns after 20 s Sufficient to cause pain within 20 s; no lethal effects Will cause no discomfort for long exposure ,

,,;,

.

.

.. . . .

.,

,

.

, .

.

.

.

In addition to the above thresholds, the Probit method is used (see above Figure 11.5.2).

208 Shock Wave Overpressure Models: For quantifying the effects of overpressure the analyst can use tables similar to the probit method as shown in Figure 11.5.2.

9.

Table 11.5.1, or

I N T E G R A T I O N OF RESULTS

The extent and the final output of the Consequence Analysis depends on the scope and the overall framework and objectives of the risk assessment approach under which it is performed. For some approaches it is sufficient to calculate the physical effect (i.e. concentration, thermal radiation, overpressure) as a function of the distance from the source for a limited number of accident scenarios. Others require a step forward in the analysis asking for the risk, expressed as the probability of fatality of an individual being at a specific point (see Section 11.2). The extent of the consequences, expressed by the expected number of fatalities as a function of the frequency of accidents scenarios (F-N curve) might also be required. Moreover, the number of accident scenarios analysed might be limited or quite large. In Quantitative Risk Assessment (QRA) in particular, an integration of the risk is required (see Section 111.1). This means that the individual results of the consequence assessment for various release categories have to be combined in order to provide final risk measures. Let k=1,2 ..... K be the release categories, with p~ the respective expected frequencies (see Section II.6), and Rk(x,y) the conditional individual risk (probability of fatality) given that the k-th release is realized. Then: K

R ( x , y ) : ~_~pk .Rk(x,y )

(6)

k=l

This risk measure presents the unconditional (or overall) risk and considers all risk sources.

10.

COMPUTER PROGRAMMES FOR CONSEQUENCE ASSESSMENT

Again, the intention here is not to give an extensive and exhaustive list of software packages for consequence assessment, but rather to inform the reader on the availability of some "typical" codes. For this reason only a limited number of codes will be mentioned. Some of the most widely known and used codes are: Two phase releases: 9 9

DEERS (Jaycor Inc.), PIPEPHASE (Simulation Sciences Inc.)

209 Heavy gas dispersion: DENZ/CRUNCH (UKAEA), CHARM (Radian Corp.), SLAB (Lawrence Livermore National Laboratory, USA), HEGADAS/DEGADIS (US Coast Guard) Complete consequence analysis (discharge-evaporation-dispersion-fire-explosionvulnerability): WHAZAN, PHAST, SAFETI (Technica Int'l), RISKAT (Health and Safety Executive - UK), EFFECTS/DAMAGE, RISKCURVES (TNO - Netherlands) SOCRATES (NCSR Demokritos - Greece)

11.

U N C E R T A I N T I E S IN C O N S E Q U E N C E A S S E S S M E N T

From the preceding analysis the reader might have gained the impression that consequence assessment is a straight-forward approach, where input variables are well-determined, taking certain (deterministic) values, models are perfectly known and deterministically describing the phenomena and, consequently, output variables are calculated with certainty, as well. Unfortunately, this is only an approximation of the reality. In fact, the whole procedure is full of uncertainties. In general, there are two types of uncertainty: uncertainty due to the stochastic nature of the phenomena, and uncertainty due to imperfect knowledge (see also discussion in Section 11.6). The first type concerns some phenomena and variables which stochastically vary in time. The weather conditions is such an example: It is not possible to predict with 100% accuracy the wind velocity and direction at a specific point in space and a specific time in the future, even if the present and the past conditions are perfectly known 2. The second type concerns the lack of information, which is present in almost every step of the analysis. Our knowledge of the phenomena following an unexpected release is not perfect and it is usually based on empirical rules and observations from a limited number of accidents. The input parameters are also uncertain since the exact conditions of the accidents can not be defined with accuracy in advance. For handling these uncertainties and imperfect knowledge the analyst has usually to make rough assumptions, introducing subjective judgement, i.e. an additional source of uncertainty, in the overall procedure. As a result, the output of the consequence assessment is characterised by the presence of many uncertainties. The analyst and the decision maker should be aware of these uncertainties associated with the results of risk assessment and take them into consideration in risk-related decisions.

However, some scientists believe that this uncertainty is due to lack of information, too. They claim that our knowledge on the system is imperfect and does not permit the detailed description and representation of the phenomena. If we had an advanced understanding and modelling of the relevant phenomena, we would be able to predict with certainty and accuracy the future weather.

210 As an example, some sources of uncertainty refer to: weather conditions, conditions within the containment (e.g. pressure, phase of the substance, quantity of the substance in the vessel at the time of rupture), size and location of the orifice, fraction of liquid drained out, droplets in the released substance, presence of ignition sources and exact time of ignition, behaviour of projectiles, vulnerability of structures and people. One way for handling these uncertainties is to repeat the calculations for all the possible combinations of the uncertain input values and all the possible variations of the models involved, assigning to them the respective probabilities. This normally leads to incredibly high numbers of scenarios to be calculated. In order to overcome that problem, either the interest is focused to only a few important variables (the others handled as certain), or some representative categories are selected, analysed in detail and the relevant expected frequencies are calculated, or a great number of scenarios are evaluated, or finally a Monte Carlo simulation approach is applied. In any case, attention should be paid to the correlation between the uncertain variables. For more details one can also refer to references [3,10].

12.

CONCLUSIONS

In this section the main models for consequence assessment have been discussed. It should be acknowledged that focus was given not to detailed descriptions of the various models, but rather the objective was to show how the models are combined with other models in order to provide quantitative measures of the consequences of accident events. For a detailed description of the models available, the reader is invited to search in the literature, which is very rich on this subject.

211 REFERENCES

,

,

~

,

o

10.

11.

Center for Chemical Process Safety (CCPS), Guidelines for Chemical Process Quantitative Risk Assessment, American Institute of Chemical Engineers, 1989. I.A. Papazoglou, M. Christou, O. Aneziris, Z. Nivolianitou, On the management of severe chemical accidents. DECARA: A computer code for consequence analysis in chemical installations, Case study: Ammonia plant, Journal of Hazardous Materials, 31, 1992. A. Amendola, S. Contini, I. Ziomas, Uncertainties in chemical risk assessment: Results of a European benchmark exercise, Journal of Hazardous Materials, 29, 1992. I.A. Papazoglou, Z. Nivolianitou, O. Aneziris, M. Christou, Probabilistic safety analysis in chemical installations, J. Loss Prevention in Process Industries, 5, 1992. I.A. Papazoglou, O. Aneziris, G. Bonanos, M. Christou, SOCRATES: A Computerized Tool Kit for the Quantification of the Risk from Accidental Releases of Toxic and/or Flammable Substances, in A.V. George (ed.): Integrated Regional Health and Environmental Risk Assessment and Safety Management (Special Issue), published in the Int. J. Environment and Pollution, 6, 1996. C. Nussey, Research to improve the quality of hazard and risk assessment for major chemical hazards, J. Loss Prevention in the Process Industry, 7, 1994. Technica Ltd., Ansaldo, Benchmark Exercise on Major Hazard Analysis, summary contribution to JRC Ispra, EUR-13597/I EN, ed. S. Contini, 1990. TNO, Committee for the Prevention of Disasters, Methods for the calculation of the physical effects resulting from releases of hazardous materials (Yellow book), CPR 14E, The Netherlands, 1992. TNO, Committee for the Prevention of Disasters, Methods for the calculation of possible damage to people and objects resulting from the releases of hazardous materials (Green book), CPR 16E, The Netherlands, 1992. I.A. Papazoglou, M. Christou, O. Aneziris, Z. Nivolianitou, Uncertainty Quantification in a Probabilistic Safety Analysis of a Refrigerated Ammonia Storage Facility, European Safety and Reliability Conference, Copenhagen, Denmark, 1992. I.A. Papazoglou, Z. Nivolianitou, O. Aneziris, M. Christou, Risk Assessment of Hydrocarbon Storage Facilities, Safety and Reliability Assessment- an Integral Approach, European Safety and Reliability Conference, Munich, Germany, 1993.

212

Risk Assessment & Management in the Context of the 'Seveso Directive' European Commission, JRC

Consequence Analysis and Modelling M.D. Christou, European Commission, DG JRC, Ispra

Outline 9 I n t r o d u c t i o n - Sources of h a r m to m a n 9 Basic steps for c o n s e q u e n c e analysis 9 Source-term models 9 Dispersion models 9 Fire m o d e l s 9 Explosion models 9 Vulnerability models 9 U n c e r t a i n t y in c o n s e q u e n c e analysis 9 Conclusions

213

%***

Sources of H a r m to Man

9 Direct e x p o s u r e to toxic s u b s t a n c e 9 T h e r m a l radiation 9 Pressure wave 9 Projectiles

Consequence Analysis Procedure

%***

r

I CONDITIONS WEATHER

I'l CONSEQUENCE OUTFLOW I~ v,PoU,l ~1DISPERSIOHN EXPOSURE ILIQuIDRATEJ

"-I MODEL~

(DOSE)

ASSESSMENT. ANALYSIS

[~] EVAPORATION I TOPOGRAPHY~,.~ EMERGENCY [ VULNERABILITY / RATE MODEL RESPONSE MODEL PLAN

214

Source-Term Models 9 Quantitative determination of the release 9 Calculation of outflow/evaporation rates 9 Depending on weather conditions 9 Specific models available Flow of liquid/vapour from a tank through an orifice Flow of liquid/vapour from a pipe rupture Two-phase flows (flashing liquids) Liquid pool evaporation/boiling -

-

-

-

Dispersion Models QUANTITY AND INITIAL CHARACTERISTICS OF THE RELEASE

I WEATHER I CONDITIONS

I TOPOGRAPHY I

CONCENTRATION OF THE SUBSTANCE AT EACH TIME AND POINT AROUND THE SOURCE c (r,w,t)

PROPERTIES OF THE SUBSTANCE

215

Dispersion Models 9 VAPOUR CLOUD BEHAVIOUR Lighter-than-air (buoyant / passive / Gaussian dispersion) Heavy gas dispersion 9 DURATION OF RELEASE instantaneous release (puff) continuous release (plume) 9 COMPLEXITY OF MODELLING - " b o x " models complex terrain (3-D) models - Computational Fluid Dynamics (CFD) -

-

-

-

-

Weather Conditions 9 W i n d velocity ( m / s ) 9 Wind direction 9 Stability class (Pasquill-Gifford) A - F ( e x t r e m e l y u n s t a b l e - e x t r e m e l y stable) 9 Ambient temperature 9 Ground temperature 9 Relative h u m i d i t y

216

#_-

Topography 9 Altitude of each point around the source (downwinds)

9 G r o u n d roughness z 0 at each point a r o u n d the source; 5 typical values, for flat terrain, agricultural land, sparse houses, residential area, and urban area (high buildings)

Gaussian Dispersion 9

FOR INSTANTANEOUS RELEASE"

., ~+-.,,,)ixt<)i ~.:>-,,

<.~.y.z~ {~.),,. <..<...<.zLOXR. ~<

9

o

ox

FOR CONTINUOUS RELEASE"

~x,y,z,; "E/
.

exp

~

~-~z+"'21}

+ exp[

2ty ~

#

217

Heavy Gas Dispersion

#

9 Releases of gases h e a v i e r t h a n air (e.g. Chlorine) 9 Releases of gases w h i c h are l i g h t e r - t h a n - a i r in n o r m a l c o n d i t i o n s (e.g. A m m o n i a ) , b u t the release takes place at c r y o g e n i c conditions 9 P h a s e s of h e a v y gas d i s p e r s i o n Initial acceleration a n d d i l u t i o n 9 Slumping Phase Passive (Gaussian) d i s p e r s i o n p h a s e

Heavy Gas Dispersion Instantaneous Release

#

9 Initial acceleration a n d d i l u t i o n - modeled as a cylinder with R=H initial entrainment of air (assumptions,..) -

9 Slumping phase puff slumping rate (dR/dt) - entrainment of air from top and edges mass balance (total mass of hazardous substance = constant) heat transfer from entrained air, ambient air, ground -

-

-

9 Passive p h a s e Gaussian dispersion transition point - virtual source -

-

218

Heavy Gas DispersionContinuous Release 9 Initial acceleration a n d dilution ~. modeled as a slice with H = W / 2 ,~ initial entrainment of air (assumptions,..) 9 Slumping phase ~ ~ ~ ~.

puff slumping rate (dW/dt) entrainment of air from top and edges mass balance (total mass of hazardous substance = constant) heat transfer from entrained air, ambient air, ground

9 Passive phase ~ Gaussian dispersion ~. transition point .. virtual source

Fire Models POOL FIRES 9 B u r n i n g rate (usually constant for given material) 9 Flame height, H (function of b u r n i n g rate a n d pool diameter) 9 Flame tilt (by the w i n d ) 9 Surface e m i t t e d t h e r m a l flux (by Stefan-Boltzmann eqn.) E 9 Geometric v i e w factor (position of receptor relative to the flame) G 9 A t m o s p h e r i c transmissivity (humidity, w e a t h e r conditions) 6 9 Received t h e r m a l flux : Q(x) = 6 E F a ( K W / m 2) 9 A t t e n t i o n for D O M I N O effect

219

%***

Fire Models

JET FIRES

9 Result from pressurised releases of flammable gases or liquids 9 Modeled as a cylinder of dimensions DxL 9 Calculation of D and L (mainly by empirical eqn.) 9 Geometric view factor 9 Calculation of received thermal flux 9 Attention for DOMINO effect

Fire Models

Boiling Liquid Expanding V a p o u r Explosion Occurs from the s u d d e n release of a large mass of pressurised superheated liquid to the atmosphere

9 BLEVE:

9 Fireball: Atmospheric burning of a fuel-air cloud in which the energy is mostly emitted in the form of radiant heat. Rises due to b u o y a n c y forces of the hot gases. 9 Effects: Thermal radiation, projectiles, overpressure (not important)

220

BLEVE

l

9 9 9 9 9 9

D

r

D = 6.48 M 0"325 Peak fireball diameter t = 0.825 M 0"26 Fireball duration Height of fireball centre H = 0.75D Surface emitted power E Geometric view factor F a Q(x) = 6 E Fa (KW/m 2) Received thermal radiation

Explosion Models 9

Explosion : A v e r y r a p i d c o m b u s t i o n , so t h a t the e x p a n s i o n of g a s e s r e s u l t s in a r a p i d l y m o v i n g pressure wave

9

D e f l a g r a t i o n : s p e e d of p r e s s u r e w a v e < s o u n d speed

9

Detonation:speed speed

9

Explosions:Confined

of p r e s s u r e w a v e > s o u n d

and Unconfined

9 UVCE : Unconfined Vapour Cloud Explosion

221

*****

UVCE

9 TNT model 9 A s s e s s the m a s s of T N T e q u i v a l e n t to the flammable material released 9 E s t i m a t e the o v e r p r e s s u r e vs. d i s t a n c e f r o m the relevant TNT curve

9 TNO

model

9 C a l c u l a t e the c h a r a c t e r i s t i c e x p l o s i o n l e n g t h L 0 9 C a l c u l a t e the o v e r p r e s s u r e vs. d i s t a n c e

*****

Accident Event Trees LPG - SPHERE

LPG RELEASE

IMMEDIATE IGNITION

DELAYED IGNITION

NO

EXPLOSION

NO.

4.

PHENOMENON

DISPERSION

222

***** %***

Accident Event Trees

#

OIL - TANK

TANK BREAK

IMMEDIATE IGNITION

No.

PHENOMENON

Vulnerability

#

9 Quantification of the undesirable effects to h u m a n health to the environment - to structures -

-

9 Depends on - the 'dose' received -

the'sensitivity' or'strength' of the receptor

9 Stochastic b e h a v i o u r , i.e. different p e o p l e e x p o s e d at the s a m e p h e n o m e n o n for the s a m e p e r i o d of t i m e m a y suffer different c o n s e q u e n c e s

223

r

r

Vulnerability

~t

9 Stochastic b e h a v i o u r 9 Time

9 LCB0" M e d i a n Lethal Concentration LD50" M e d i a n Lethal D o s e IDLH" Intermediate D a n g e r o u s for Life and Health 9 Probit function

Dose

*****

Vulnerability 9

Toxic substances Pr obit = a + b I n ( D )

where

9

D = i c" (t)dt o

Flammables

- Thermal

Probit = - ] 4 . 9 + 2 . 5 6 I n ( D )

where

9

Pressure

D =t Jo

14/3(t)dt 104

wave

Pr obit = - 18.1 + 2.79 l n ( A p )

radiation

r

224

Uncertainties related with Consequence Analysis

r

Sources of uncertainty : weather conditions release time, details and conditions / size and location of the orifice m imperfect modelling ~presence of ignition sources and exact time of ignition ~behaviour of projectiles ~vulnerability of structures and people Modelling uncertainty : m Repeat the calculations for all combinations of random variables re(for wind direction) "Rotate' the consequences according to the wind rose, taking into account the respective frequencies Monte-Carlo methods

Conclusions 9 Consequence Analysis is a basic step of Risk Assessment aiming at the estimation of the extent of the undesired effects of major accidents 9 Various models are e m p l o y e d for the simulation of the physical p h e n o m e n a following the unexpected release of h a z a r d o u s substance or energy 9 The vulnerability of people and structures presents a stochastic behaviour, usually m o d e l l e d by the probit equation 9 Uncertainties are associated with Consequence Analysis both concerning stochastic nature a n d incomplete k n o w l e d g e of the p h e n o m e n a

225

CONSEQUENCE ANALYSIS AND MODELLING EXERCISE

Exercise 1:

Suppose that as a risk analyst you have to assess the consequences of an accident scenario related to a plant. The main parts of the plant subject to the assessment are: a cylindrical tank for the storage of fuel oil, for the energy requirements of the installation, a spherical tank used for the storage of liquefied chlorine under pressure. The first accident scenario concerns the rupture of the fuel oil tank. It should be mentioned that there is a dike around the tank, ignition sources might be present, and there are pumps within the dike's area which can be used in the case of emergency. However, in order to assess the potential consequences you make the assumption to ignore these pumps in your analysis. The second accident scenario concerns a rupture at the upper part of the chlorine spherical tank. In the literature you find that both liquid and gaseous chlorine is likely to be released in this case.

%

From a set of available models choose the proper ones in order to perform a complete consequence analysis. Which models are you going to use for the evaluation of the first accident scenario and which for the second? Put the models in their right order of use, so that the output of one can be used as input for the next model. Make a simple logic diagram of the steps to be followed in order to assess the consequences. Do you need meteorological data for your assessment?

Available models: Gaussian dispersion model gas outflow model two-phase outflow model UVCE - TNO model probit for toxic effects fragments projection model

evaporation model liquid outflow model Heavy gas dispersion model TNT equiv. UVCE model BLEVE probit for overpressure

pool fire model vulnerability model jet fire model 3-D dispersion model probit for thermal effects

Solution to Exercise 1:

For the first accident scenario (rupture of the fuel oil tank), the following models are required:

Liquid ouOqow model - Pool fire model - Vulnerability model and especially the probit function for thermal effects.

226 The first phenomenon connected with this accident scenario is the release of the dangerous substance from its containment. Since fuel oil is in liquid phase, the first model to be employed is a liquid outflow model. The output of this model is the discharge rate as a function of time. Next, the released oil is collected in the dike forming a pool. The amount of fuel oil present in the dike is calculated by using simple mathematics. Assuming that an ignition source is present, this pool of flammable liquid is ignited. In order to calculate the effects of the fire, and especially the thermal radiation, for each point around the pool and as a function of time, a pool fire model should be employed. Meteorological data - and especially the wind velocity and direction- are required in order to calculate the 'tilt' of the flame. Finally, for assessing the final risk, a vulnerability model should be applied, consisting of the probit function for thermal effects. This model transforms the profile of thermal dose over the exposure time into a probability of fatality (number between 0 and 1). Ground roughness is irrelevant with the whole phenomenon. For the second accident scenario (rupture of the spherical chlorine tank), the following models are required:

Two-phase outflow m o d e l - Evaporation m o d e l - Heavy gas dispersion model or 3-D dispersion model - Dose calculations - Vulnerability model and especially the probit function for toxic effects. As mentioned in the literature, both liquid and gaseous chlorine will be released; thus, a twophase outflow model should be employed for modelling the release. The output is the discharge rate as a function of time. Next, the liquid portion of the release will be evaporated, therefore, an evaporation model is required. Since chlorine is a heavier than air gas, a heavy gas dispersion model comes next. A 3-D model can also be applied. The dispersion model gives the concentration of chlorine at any point around the tank as a function of time. From this, the dose received by an individual for the whole exposure period can be calculated (dose calculations) and by applying a vulnerability model consisting of the probit function for toxic effects, the risk (i.e. probability of fatality) is calculated. Meteorological data (wind velocity and direction, stability class, ambient temperature and humidity) are required for dispersion calculations. Ground roughness is also an input parameter for the dispersion model.

227

Exercise 2:

Suppose that as the advisor on risk issues of a local community you have to elaborate the emergency response plan for an accident scenario concerning the release of ammonia. Since there are limited resources, you have to decide whether - in the case of an emergency - you will advise people to stay at a point where the concentration is expected to be at level (3 for a time period of T, or to stay at a point where the concentration is at level 2(3 and keep the people there for a time period of T/2. The probit function for ammonia is t~

P = -15.9 + 1.85 ln(c20

Explain and justify your choice.

Solution to Exercise 2:

Without doubt, the decision will be based on risk considerations. The level of risk is higher when the value of the probit function is higher. The latter is higher when the quantity c Zt (dose) is higher. Therefore: 9 1st case: concentration Cl= C , exposure time t,= T ~

dose D1 = CZT

9 2nd case: concentration c2= 2(3, exposure time t2- T/2 ~

dose D2 = (2(3) 2 (T/2) = 2(32T

Since in the second case the dose is higher, the probit value is also higher and the probability of fatality (individual risk) will also be higher. As a general conclusion, it is preferable for a group of people to stay at a point with lower concentration even for a somehow prolonged period than to stay at a "hot spot" (i.e. places with high concentration levels) even for short period. This is also a lesson for the emergency services, that is to avoid "hot spots" even if the population has to be transferred to places where the concentration is just low, but not zero.

228 Exercise 3:

You have to assess the consequences from an accident scenario involving liquefied ammonia. You are especially interested in calculating the consequences within the installation (e.g. to ensure that the control room or specific important places will not be on risk).

%

Which dispersion model would you apply? the Gaussian model, a heavy gas fiat-terrain dispersion model (box model), or a 3-dimensional complex terrain model.

Solution to Exercise 3:

The selection of the appropriate model depends on two parameters: the density of the cloud formed (i.e. whether it is lighter or heavier than air) and the topography of the ground. In ambient conditions, ammonia is a lighter than air gas. However, in order to choose the adequate dispersion model, an analysis of the phenomena is required: As soon as the liquefied ammonia (boiling point -39C) is released to the air, it will absorb heat from the air in order to increase its temperature and to be evaporated. For some time following the release, there will be both liquid and gaseous ammonia. In addition, the air which is in contact with the cloud will become colder and some amount of water (humidity) will become liquid. The cloud formed will contain: 9 9 9 9

ammonia in gaseous phase ammonia in liquid phase, in the form of droplets air, and (liquid) water, in the form of droplets.

The whole mixture behaves as a heavier than air gas. For this reason not applicable. Moreover, we are interested in modelling the dispersion installation, probably taking into consideration the various obstacles The terrain of application is complex, and therefore, the 3-dimensional is more adequate for modelling the ammonia dispersion.

the Gaussian model is of ammonia within the and buildings present. complex terrain model

229

Exercise 4: You have performed the consequence assessment and calculated the conditional risk versus distance curve, which is depicted in the following Figure ll.5.Ex.1. This curve is independent of the wind direction, depending only on the speed of the wind, which you have assumed to be 2 m/s. There are two communities within 2 km from the installation: Community A, with 100 people, is located at a distance of 500m North of the installation, Community B, with 300 people, is located at a distance of 900m East of the installation. The frequency of a wind blowing towards North is 10%, whereas the frequency of a wind blowing towards East is 30%. Construct the F-N curve for this example.

Figure ll.5.Ex.l" Conditional Risk Versus Distance

Conditional Risk vs. Distance 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0

i

i

l

200

400

600

L

800

1000

1200

Dinstance downwinds (rn)

1400

1600

1800

2000

230 Solution to Exercise 4:

Let's analyse the case when each community is in risk. Case A: The wind is blowing towards North and community A is in risk. Frequency of the scenario: f~=0.1 From the risk vs. distance curve we see that conditional risk at 500m is R~=0.9. Given that the population of the community is 100 people, the expected number of fatalities is N1 = 0.9 x 100 = 90. Summarizing this scenario, we have N~=90 fatalities with frequency fi=0.1. Case B: The wind is blowing towards East and community B is in risk. Frequency of the scenario: f2=0.3 From the risk vs. distance curve we see that conditional risk at 900m is Re=0.5. Given that the population of the community is 300 people, the expected number of fatalities is N2 = 0.5 x 300 = 150. Summarizing this scenario, we have N:= 150 fatalities with frequency fe=0.3. The F-N curve is constructed as follows:

Exercise 4: Societal Risk (F-N curve)

0.8 >' 0 p,

0.6

0"

9

M.

0.4

i

0.2

,~.

50

.

.

.

.

.

.

t

100

.....

I v

150

Expected Number of Fatalities

200