Risk Calculations
4.1.2.1. Analytical Approach
The model is an analytical model used to calculate the risks associated with hydrogen hazards developed following QRA procedure given by several authors. One of the procedures was given by [205]. They developed a model called MPACT (population impact of toxic and flammable effects) model implemented in the SAFETI DNV software. The MPACT is a mathematical model that calculates a number of results relating to the impact on the land and population potentially affected by the various toxic and/or flammable events that are defined as inputs by the user. It employs the assumption that each event can be treated independently from other events. This assumption can be made because the frequency of accidental releases in the chemical industry is very low in comparison with the duration of the hazardous effects themselves. The integration of the risk from all possible events can, therefore, be built up event by event and this is one of the principles underlying the MPACT algorithm.
Physical Data
Release location
Weather Data
Weather Data
Event Tree Analysis
Wind speed/stability ^Effect Zones Wind directions
Reliability Database
Event Tree Analysis
Fault Tree Analysis
Outcome probabilities
Risk v Calculation ] Model
Outcome probabilities
Accident frequencies
Population Data
Population Data
Individual risk
Case data
Individual risk
Fig. 4.20 The risk calculation model environment modified from [205]
Based on this algorithm the model combines the consequences of hydrogen related accidents to the population and their frequencies. The accident consequences of hydrogen (i.e. fire and explosion outcomes) in terms of their effect zones (distances), as one of the model inputs were calculated using PHAST (section 4.5), and the result is presented in Section 5.4. Since the model is concerned with risk it also needs frequencies for each possible event and outcome. Within the model the frequency of each outcome is calculated from the frequency of the event itself and the probabilities defined on each branch of the event tree. The event frequencies of the system were simulated using the Fault Tree Analysis program developed by [86], as well as by using historical statistical data (section 4.4). The estimated frequencies are presented in section 5.3. Finally, superimposes them on the population to calculate the risk for fatalities in the surrounding area. The results are presented as FN curve for societal risk and individual risk profiles. Fig. 4.20 shows the relationship between the risk calculation model and its input and output.
The number of people (N) affected by each accident outcome is given by
x, y where, A is fatal effect area [m2] of the outcomes (see section 4.5.5), D is the population density [Pop./m2], andpf,i is probability that incident outcome case i will result in a fatality at location x, y (fatality level). Additionally, the program also calculates rate of death (1/yr), which is the weighted number of fatalities per year, given by:
All mod el o and the "Okrent" number given by:
All mod el o
The "Okrent" number is a risk measure that reflects the greater impact on society of accidents that cause high numbers of fatalities. The factor of 2 is known as the aversion index.
4.1.2.2. Drawing Risk Profile
Once risks have been calculated, the risks can be defined in terms of the complete set of triplet of numbers (s1,f1,c1) [125, 242]:
In eq. (418) st describes an accident scenario, f is its expected frequency of occurrence, and ct represents the consequences, i.e. category and magnitude of damage. "n" is the number of scenarios taken into account in determining the risk. Theoretically, n would be arbitrarily large, since many scenarios are conceivable. In practice, however, the scenarios are not taken into account if they are unlikely.
Si 
fi 
Ci 
Cumulative fi 
Si 
1  
S2 
f2 
C2 
if>I f2 1 1 
Sn1 
II  
sn 
fn 
cn 
0 
In order to presents the estimated risks as individual and societal risk (FN curve), the triplet can be transformed into the risk profiles by means of socalled "complementary cumulative distribution function (CCDF)". To create a risk profile, the triplets must be ordered in increasing order of consequence, i.e. so that ci < ci+1, as described in the Table 415. The risk profile can be plotted as a step function as in Fig. 4. 21.
Consequence value, q Fig. 4.21 FN or FC curve complementary probability distribution [125]
The individual risk (IR) profile is a twodimensional (risk vs distance) graph, and is plot of IR as a function of distance from the risk source (i.e. effect distance, z). The IR is plotted as a logarithmic plot ("semilogy"). Meanwhile, the societal risk (SR) is known as an FN curve. The FN curve is a plot of cumulative frequency vs consequences (expressed as number of fatalities). A logarithmic plot ("loglog") is used because the frequency and number of fatalities range over several orders of magnitude.
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