Quantitative Risk Analysis

CHAPTER 11

Quantitative Risk Analysis 11.1 Introduction The tools required for estimating the consequences of accidents are mathematical models for predicting accident effects (thermal radiation, overpressure, dose) and vulnerability models. The final risk is determined by multiplying these consequences by the frequency of the accidents over time. The ultimate aim of risk assessment for a given case, such as a process plant located close to an urban area, is to calculate the distribution of risk over the affected area by estimating the existing hazards and the consequences of the different accident scenarios and by applying the appropriate frequencies or probabilities. Quantitative risk analysis (QRA) consists of a set of methodologies for estimating the risk posed by a given system in terms of human loss or, in some cases, economic loss. Major accidents with severe consequences continue to occur despite the systematic application of classic safety measures such as engineering codes and checklists. QRA provides an advanced and complementary approach that can be considered a further step towards safer industry. The first milestones in the QRA of handling, storing and processing hazardous materials are the two Canvey Reports developed by the UK Health and Safety Executive [1,2] and the Rijnmond Report, issued by the Rijnmond Public Authority [3]. These studies were commissioned by public authorities in response to industry and public concerns about the risks posed by large concentrations of hazardous materials in handling and storage facilities. The Canvey Reports made a significant contribution, particularly in the field of accident frequencies, which were obtained statistically from historical data or by expert judgment. The Rijnmond Report gathered a large amount of failure frequency data and showed a high level of efficiency in presenting results, which were shown as f
N curves and risk contours. Various publications provide information on QRA methodologies. Three of the most important examples are the “Purple Book” [4], the Bevi Reference Manual [5], and the Guidelines for Chemical Process QRA [6]. In this chapter, the essential concepts associated with individual and societal risks and risk mapping are presented. Basic data on the frequency of loss-of-containment events are provided and the most common accident sequences that lead to the different accident

Evaluation of the Effects and Consequences of Major Accidents in Industrial Plants. DOI: http://dx.doi.org/10.1016/B978-0-444-63883-0.00011-3 © 2018 Elsevier B.V. All rights reserved.

439

440 Chapter 11 scenarios are considered. Two simple examples are used to illustrate the essential aspects of QRA procedures, which apply the concepts of individual and societal risk and make only a brief reference to the calculation of effects and consequences. Then, the QRA methodologies and the mathematical models discussed in the previous chapters are applied to a real case.

11.2 Quantitative Risk Analysis Steps QRA is based on the application of mathematical models to determine the consequences of previously identified accident scenarios and on the use of the corresponding frequencies to estimate the resulting risk over a given area. QRA is performed through a series of steps or activities which are schematized in Fig. 11.1 [7]. The first step is to gather all of the relevant information. This may include geographical information about the location of the studied area: whether it is level or mountainous, the presence of rivers, its latitude and longitude, etc.; climate data: humidity, solar radiation, wind direction and velocity (wind rose), atmospheric stability, etc.; the physical and chemical properties of the substances involved; and, finally, information about the process and the plant or system analyzed. Once this information has been obtained it is possible to identify the different hazard scenarios that must be considered: a hole in a pipe, a full pipe rupture, the explosion of a vessel, etc. Simplifying guidelines have been proposed for generic risk analysis (see Chapter 2: Source Term, Section 8). Once the possible types of release have been identified it is necessary to estimate their respective frequencies. This can be done by using fault trees or generic data obtained from various sources (see Chapter 9: Determination of Accident Frequencies). Each release type leads to diverse sequences which, in turn, cause different types of accident. Therefore, it is necessary to develop the corresponding event trees (Chapter 9: Determination of Accident Frequencies). By introducing the corresponding probability at each branch in the sequence it is possible to estimate the frequency of the different accident scenarios. The following nomenclature is used. The initiating event, for example the rupture of a pipe, is an incident. The physical result of an incident, for example the generation of a toxic cloud, is an accident; the accident can evolve according to an accident sequence, which can lead to several potential accident scenarios. Finally, the accident scenario is one of several specific situations at the end of an accident sequence, such as the development of a toxic cloud in a given direction.

Quantitative Risk Analysis 441 Collection of relevant information Geographical situation

Climate data

Physical and chemical data of products

Technical data about the process or system analyzed

Hazard scenario identification

Frequency estimation

Event trees (with probability data)

Effects and consequences analysis

Estimation of individual risk

Estimation of global risk for the population

Figure 11.1 Main steps in a quantitative risk analysis.

442 Chapter 11 Mathematical accident models and vulnerability models must be used to calculate the effects and consequences of each accident scenario. By combining the consequences with their corresponding frequencies we can obtain the individual risk (IR) at any desired distance and plot iso-risk curves. Once we know the IR at any point it is possible to estimate the overall risk to the population.

11.3 Individual and Societal Risks Risk is a function of the frequency of an accident and the magnitude of its consequences. The possible consequences are injury to the population or economic losses. QRA often takes into account human loss. The possible types of harm to people are injury or fatality. However, a significant amount of additional work is required in order to analyze injuries (e.g., second-degree burns or harm due to a toxic gas) and a significant level of uncertainty affects the analysis in the case of multiple hazards. As a result, most risk assessments only consider fatal effects. The following definitions of individual and societal risks and the risk contour maps are based on fatal effects.

11.3.1 Definition of Individual and Societal Risks The results of QRA for human loss are often expressed as individual and/or group or societal risks. IR is the risk to a person located (24 hours/day, 365 days/year) in the vicinity of a hazard [8]. This definition includes the nature of injury to the individual, the probability of each type of injury and the time period during which the injury may occur. If IR is expressed in terms of fatalities it can be defined as a function of spatial coordinates which represent the probability that an individual at a fixed outdoor point during a 1-year period will die as a result of an accident at a plant, installation or transport route. The unit used to measure IR is year21. IR at a given location can be expressed as [6]: IRx;y 5

i5n X

IRx;y;i

(11.1)

i51

where IRx,y is the total IR of fatality at the geographical location x, y (frequency of fatality per year and per person), IRx,y,i is the IR of fatality at the geographical location x, y under accident scenario i (frequency of fatality per year or year21), and n is the total number of accident scenarios considered in the analysis.

Quantitative Risk Analysis 443 IRx,y,i can be expressed as a function of frequency and probability: IRx;y;i 5 fi UPFi

(11.2)

where fi is the frequency of the accident scenario i (year21) and PFi is the probability that the accident scenario i will result in a fatality at location x, y. The value of PFi is obtained by applying the accident effects models and vulnerability models. Finally, fi is calculated from the frequency of the incident (initiating event) and the probability that the sequence of events leading to the accident scenario i will occur: fi 5 fincident i UPsequence i

(11.3)

where fincident i is the frequency of occurrence of the incident or initiating event (year21) and Psequence i is the overall probability of the sequence of events that lead to the accident scenario i (
). Initiating events with a frequency of less than 1  1029 year21 are not usually considered in QRA. The same applies (when calculating the risk to the external population) to accidents where the distance at which the probability of lethality is 1% is within the limits of the plant. Major accidents can affect areas in which a large number of people are concentrated. In these cases the societal risk is used to measure the risk to a group of people. Societal risk is the expected number of casualties per year measured in casualties  year21. It is calculated using demographic data for a given area: ð Societal risk 5 ðindividual riskÞ  ½population density ðx; yÞ dx dy (11.4) When estimating the societal risk in a given area it is possible to consider specific parameters such as time-of-day effects (different situations during the day or at night, for example), day-of-week effects (working days or weekends) and the protection provided by shelter (people indoors will be protected against certain accident scenarios). Finally, average IR can be calculated as the average of the IR of all people exposed to risk from a given facility. It is very important to know how this population has been selected, as the inclusion of people at low or no risk can introduce a significant bias. Average IR is often calculated for the exposed population, but it could also be calculated for the total population in a given area without taking into account whether all or only some of the people are exposed to risk from the facility. This can significantly lower the value of the average risk. The average IR for the exposed population is calculated as [5]: X X IRav 5 IRx;y Upx;y = px;y (11.5) x;y

x;y

444 Chapter 11 where IRav is the average IR (exposed population) (year21) and px,y is the number of people in location x, y (
). The average IR can also be expressed (mainly for employees) as the fatal accident rate, i.e., the number of fatalities per 108 person-hours of exposure.

11.4 Risk Mapping 11.4.1 Individual Risk Contours IR contours or iso-risk curves represent the levels of IR around the installation analyzed. An iso-risk curve connects all of the geographical locations around a hazardous activity with an equal IR, i.e., all of the locations with the same overall probability of lethality. This is the clearest and most common way of producing a graphical representation of the risk over a given area. In order to produce an iso-risk curve it is necessary to calculate the respective contributions of different accident scenarios, each of which has its own probability and lethality: the resulting overall risk is the sum of the risks corresponding to each one of the accident scenarios. In order to establish the iso-risk curves, it is necessary to perform the calculations corresponding to [9] • • • •

the different accident scenarios (hole in a pipe, collapse of a tank, etc.), the different reactions of the system to a particular incident (system failure, operator intervention, etc.), the different meteorological conditions (atmospheric stability, wind direction/speed), the different ignition locations and times.

IR contours can be circular if the physical effects of the accidents spread uniformly in all directions or more irregular if the intensity of the effects differs according to the direction. We can therefore distinguish between radial risk and directional risk. Radial risk produces circular iso-risk curves, where the value of risk decreases with the radius. Accident scenarios typically associated with this type of risk are fire, BLEVE, other vessel explosions and certain vapor cloud explosions: thermal radiation and overpressure essentially spread uniformly in all directions. Directional risk produces irregular iso-risk curves due to the nonhomogeneous distribution of wind direction as a function of time (wind rose), the various possible grades of atmospheric stability and certain physical directional parameters. The accident scenarios associated with this type of risk are the atmospheric dispersion of flammable or toxic substances or the ejection of missiles in the explosion of cylindrical vessels.

Quantitative Risk Analysis 445 When radial and directional risks overlap, the overall iso-risk curves are obtained by adding the risks corresponding to each accident scenario and the shape of the curve is altered accordingly.

11.4.2 Procedure The following steps are used to calculate the IR curves (Fig. 11.2): 1. Define a mesh of points in which to calculate the IR. The mesh must include the activity/plant analyzed and should cover at least the maximum distance over which

Figure 11.2 Procedure for the calculation of the IR curves.

446 Chapter 11

2. 3.

4.

5.

any lethal consequences of the accident scenarios are observed. Mesh cells are usually 25 3 25 m for distances of less than 300 m and 100 3 100 m for larger distances. Establish coordinates (x, y) for the point at which the accident scenario (j) originates. Establish the frequency (fji) of the initiating event for this accident scenario. Establish meteorological data: stability class and its corresponding probability (PM). A value of 0.8 is usually assumed for class D and 0.2 for class F. Establish the probability of the wind direction for each sector (wind rose) (Pw). P 5 1 for accident scenarios that produce thermal radiation. Determine the probability of the final accident scenario (Pjf). Determine the area covered by lethal effects and the probabilities of death (Pd) for each stability class and wind direction for each mesh point. Calculate the contribution to IR (ΔIRji,jf,M,w) for the accident scenario considered, including the frequency of the initiating event, the probability of the final accident scenario, the probability of the stability class, the probability of the wind direction and the probability of death at a given point of the mesh: ΔIRji; jf;M;w 5 fji  Pjf  PM  Pw  Pd

6. The overall individual risk (IR) at a given point of the mesh is: XXXX IR 5 ΔIRji; jf;M;w ji

jf

M

(11.6)

(11.7)

w

This calculation process is shown in Fig. 11.2. Iso-risk curves are usually plotted for orders of magnitude. It is a fairly complex process which is usually performed by applying appropriate computer codes [10]. The following section provides an example of the calculation process for the IR at a given point (see also Section 11.6).

11.4.3 Societal Risk Societal risk can be also presented as f
N curves. These are obtained by plotting the cumulative frequency (f) of accident scenarios that cause N or more fatalities per year as a function of N (usually on a log
log scale). In order to calculate a societal risk f
N curve, it is important that the frequencies and the number of fatalities are combined correctly. The number of fatalities Ni from each accident scenario is X Ni 5 px;y UPFi (11.8) x;y

where px,y is the number of people at location x, y (
) and PFi is the probability that the accident scenario i will cause a fatality at location x, y (
).

Quantitative Risk Analysis 447

Figure 11.3 f
N curve for a propane dehydrogenation plant.

The number of fatalities and the associated frequency must be estimated for each accident scenario. The data are then expressed as cumulative frequencies with X fN 5 fi for all accidental scenarios i for which Ni $ N (11.9) i

where fN is the frequency of all accident scenarios with N or more fatalities (year21), fi is the frequency of accident scenario i (year21), and Ni is the number of fatalities in accident scenario i (
). f
N curves are mainly used in land use planning to ensure that residential areas, schools, hospitals and other public spaces fall outside specific risk contours. Fig. 11.3 shows an example of an f
N curve for a given chemical plant. Obviously, the frequency decreases as the number of fatalities increases, i.e., the accidents that cause a large number of fatalities occur far less frequently than accidents that cause few fatalities.

11.5 Introductory Examples of Risk Calculation Three simple examples are used to illustrate the concepts described in the previous sections: the first is a general case involving several accident scenarios and the second deals with an explosion in a specific unit.

448 Chapter 11 Example 11.1 A pharmaceutical substance is solved in ethanol (20% mass). 300 kg h21 of this solution must be dried to a humidity of 0.05 kg (kg dry solid)21. Drying must be performed in a spray drier, using 1110 kg h21 of dry air, previously heated. (1) Calculate the concentration of ethanol in the exit air (at 70 C). Will the operation be correct? (2) In case of an explosion, two operators would die. At the plant there are 70 workers per shift (two shifts of 8 hours, 250 days per year). The plant has been working for 10 years, without any previous accidents. Calculate the value of the FAR after the explosion, and the frequency (fatalities per person and year). Data: vaporization heat of ethanol 5 850 kJ kg21. Solution 1. 300U0:2 5 60 kg h21 of dry solid 300 2 60 5 240 kg h21 of ethanol 60  0.05 5 3 kg of ethanol in the dried solid Vaporized ethanol: 240 2 3 5 237 kg h21 Volume: 237 kgU22:4 m3 kmole21 ð273 1 70Þ 5 145 m3 h21 46 kg kmole21 273 Air flow rate at exit: 1110 kg h21 U0:98 m3 kg21 5 1088 m3 h21 c5

146:2 5 0:118 m3 m23 ; i:e:; 11:8% volume 146:2 1 1088

Flammability limits for ethanol/air mixtures: 3.3%
19% volume: the operation would not be safe. 2. Time worked at the plant over the last 10 years: 70  ð2  8Þ  250  10 5 2:8  106 hUperson FAR 5 Frequency 5

2  108 5 71:4 2:8  106

8  250  71:4 5 0:0014 fatalities person 21 year21 108

Quantitative Risk Analysis 449 Example 11.2 Consider a processing plant in which the following possible incidents have been identified: 1. The release of a toxic gas due to the full-bore rupture of a pipe (length: 4 m). 2. The release of a flammable gas due to the catastrophic failure of a vessel. The following simplifying hypotheses are assumed: G

G

G

Both events are caused at the center of the plant. Only two typical weather conditions are present: the atmospheric stability is constant and wind blows from the north (70% of the time) or from the east (30% of the time). The probability of death due to an accident at a given location is either 0 or 1.

Additional data (Table 9.2): frequency of vessel catastrophic failure: 5  1026 year21; frequency of rupture of a pipe: 3  1027 m21 year21; probability of ignition of a flammable cloud: 0.5. Estimate both the individual and the societal risk for the population distribution in the area shown in Figs. 12.5 and 12.6. (Note: this example is based on the case published by Hendershot [11]). Solution The event trees in Fig. 11.4 show the various accident scenarios that can occur and their respective frequencies. The possibility of a flash fire in the case of a flammable gas release is not considered. For Event 1, the probability that the plume moves in a certain direction is not usually included in the event tree but instead is considered in a later step; here this probability has been included in order to provide a clearer picture of all possibilities considered.

Figure 11.4 Event trees and frequency estimations for the two incidents considered. (Continued)

450 Chapter 11 Example 11.2 (Continued) The frequencies of each accident scenario are calculated by multiplying the frequency of the initiating event by the probabilities of each branch: ftoxic

cloud to south 5 (3  10

ftoxic

cloud to west 5 (3  10

27

)  4  0.7 5 8.4  1027 year21

27

)  4  0.3 5 3.6  1027 year21

fexplosion 5 (5  1026)  0.5 5 2.5  1026 year21. Now the effects and consequences must be established for each accident scenario. After applying accident and vulnerability models, assume that the following consequences are estimated for each accident scenario: G

G

Toxic cloud (both to the south and to west): all people in a circular sector of radius 200 m and 20 width are killed (probability of death 5 1) and all people outside this area are unaffected (probability of death 5 0). Explosion: all people within 130 m of the explosion center are killed (probability of death 5 1) and all people beyond this distance are unaffected (probability of death 5 0).

Fig. 11.5 shows the areas covered by each accident scenario and the facility contour. In some areas the effects of more than one scenario overlap (Areas III and IV, which are subjected to both the explosion and the toxic cloud). The IR from an accident scenario in a given area can be calculated by multiplying the probability of death (P 5 1) by the frequency of the scenario. In areas affected by more than one accident scenario the IRs corresponding to each scenario are added to obtain the total IR. For example, in Area IV: IRIV 5 8:4  1027 1 2:5  1026 5 3:34  1026 fatalityUperson21  year21 Table 11.1 shows the total IRs for the various areas. Fig. 11.5 shows the risk contours corresponding to these IR values. In QRA, IR contours are usually plotted for orders of magnitude of risks (1024, 1025, etc.). Assume the distribution of people shown in Fig. 11.6. These people are subject to the risk covering each area. Consequently, the 14 people located to the south-east beyond the distance reached by the lethal effects of the explosion are not exposed to any risk, while the 12 people located further to the south (Area VI) are exposed to a certain degree of risk. The average IR to the population subject to risk is therefore calculated as IRav 5

            4 2:5U1026 1 3 2:5U1026 1 8 3:34  1026 1 4 3:34  1026 1 6 3:6  1027 1 12 8:4  1027 4 1 3 1 8 1 4 1 6 1 12

5 1:89U1026 year21

(Continued)

Quantitative Risk Analysis 451 Example 11.2 (Continued)

Figure 11.5 Individual risk contour map (the dotted line represents the facility boundary). Table 11.1: Total individual risk corresponding to each area. Area I II III IV V VI

Accident Scenarios

IR (year21)

2-a 2-a 2-a, 1-b (west) 2-a, 1-a (south) 1-b (west) 1-a (south)

2.5  1026 2.5  1026 2.86  1026 3.34  1026 3.6  1027 8.4  1027

If the calculation is based on the total population in the area (including the 14 people not subject to any risk) the average IR is IRav 5

            4 2:5  1026 1 3 2:5  1026 1 8 3:34  1026 1 4 3:34  1026 1 6 3:6  1027 1 12 8:4  1027 4 1 3 1 8 1 4 1 6 1 12 1 14

5 1:37U1026 year21

However, it is more common to calculate the IR on the “external” population, which excludes the employees inside the plant contour. In this case the IR to the affected population would be calculated as       6 3:6  1027 1 4 3:34U1026 1 12 8:4  1027 IRav 5 5 1:16  1026 year21 6 1 4 1 12 (Continued)

452 Chapter 11 Example 11.2 (Continued)

Figure 11.6 Distribution of population in the accident area (* indicates employees). Table 11.2: Estimated number of fatalities for each accident scenario. Accident Scenario 1-a (south) 1-b (west) 2-a 2-b

f (year21) 27

8.4  10 3.6  1027 2.5  1026 2.5  1026

Number of Fatalities (N) 16 6 4 0

The average IR to on-site employees is       4 2:5  1026 1 3 2:5  1026 1 8 3:34  1026 5 2:95  1026 year21 IRav 5 41318 However, this is not an interesting value, as (1) employees do not work 24 hours per day, 365 days per year and (2) they are exposed to additional risks due to their activities. Therefore, IRav should not be used to calculate the fatal accident rate for employees. Typically, for a process plant operator FAR  4; the risks are originated by major accidents (50%) and by conventional risks (50%). The f
N curve is used to represent the societal risk. It is necessary to know the estimated number of fatalities (external population) corresponding to each accident scenario (Table 11.2) in order to plot the curve. (Continued)

Quantitative Risk Analysis 453 Example 11.2 (Continued) The data in Table 11.2 can be used to calculate the cumulative frequency (Table 11.3) as a function of the number of fatalities. This is done by rearranging the accident scenarios according to descending number of fatalities and calculating the frequency of N or more fatalities. We can now plot these data on a logarithmic scale to obtain the f
N curve (Fig. 11.7).

Table 11.3: Cumulative frequency data. Estimated Number of Fatalities (N) .16 16 6 4

Accident Scenarios Included

f (year21)

Cumulative Frequency (year21)

None 1-a (toxic cloud to S) 1-b (toxic cloud to W) 2-a (explosion)

0 8.4  1027 3.6  1027 2.5  1026

0 8.4  1027 1.2  1026 3.7  1026

Figure 11.7 Societal risk f
N curve.

454 Chapter 11 Example 11.3 A potential explosion hazard caused by the accumulation of propane in the flammability range has been identified by applying HAZOP to a processing plant furnace. The dimensions of the furnace chamber are 10 3 20 3 5 m. 1. Calculate the maximum amount of propane which could accumulate in flammable conditions at ambient temperature (cool furnace) and estimate the intervention area and the alert area to be considered in the event of an explosion. 2. The frequency of explosion in the furnace has been estimated as 3  1025 year21. Assuming continuous operation during the whole year, calculate the distance at which the direct effects of the explosion yield an IR of 1026 year21. 3. Assuming a lethality of 100% for ΔP $ 0.3 bar (as often done in standard quantitative risk analyses) calculate the zone covered by this lethality. Assume that the intervention distance (di) is the distance at which ΔP 5 0.125 bar and that the alert distance (da) is the distance at which ΔP 5 0.05 bar. Additional data: flammability limits for propane (Table 3.1): 2.1%
9.5% volume; Mw propane 5 44 kg kmole21; ambient conditions: temperature 5 25 C, pressure 5 101.325 kPa. Solution 1. Maximum amount of propane in flammable conditions: V 5 0:095  ð10  20  5Þ 5 95 m3   101:325 U103 44 PMw  5 95  Vρ 5 V 5 171 kg of propane RT 8:314  103  ð273 1 25Þ The relationship between ΔP and the distance is established by applying the equivalent TNT method (Chapter 4: Vapor Cloud Explosions): pffiffiffiffiffiffiffiffiffiffiffi di 5 3 WTNT d n sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M ΔHc 3 da 5 η d n 5 3 0:03  171  10 Ud n ΔHTNT dn can be obtained from Fig. 4.4 for the two values of ΔP: ΔP 5 0:125 bar . dn 5 12 m kg 21=3 ΔP 5 0:050 bar . dn 5 24 m kg 21=3 Therefore, ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p 3 0:03  171  10  12 5 45 m ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p da 5 3 0:03  171  10  24 5 89 m di 5

(Continued)

Quantitative Risk Analysis 455 Example 11.3 (Continued) 2. By applying Eq. (11.2), 1026 5 3  1025 PFi PFi 5 0.033 . a probability of 33 fatalities per 1000 exposed people. The corresponding probit variable is (Table 8.1) Y 5 3:16 By applying the probit expression for death due to the overpressure direct effects (pulmonary hemorrhage) (Eq. (8.16)), 3:16 5 2 77:1 1 6:91 ln ΔP ΔP 5 110; 750 Pa ðor 1:1 barÞ The scaled distance is obtained from Fig. 4.4: dn 5 3.2 m kg21/3 Therefore, the distance at which IR 5 1026 year21 is pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d 5 3 0:03  171  10  3:2 5 12 m This is very close to the furnace. At this distance, the risk posed by the indirect effects of the explosion (body displacement, fragments) would be much higher than the risk due to direct effects. 3. A value ΔP 5 0.3 bar corresponds to a scaled distance (Fig. 4.4) dn 5 6.7 m kg21/3. The distance reached by a lethality of 100% (assuming the aforementioned threshold of 0.3 bar) would be pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d 5 3 0:03  171  10  6:7 5 25 m This means a circular area with this radius.

11.6 Example Case Example 11.4 A cylindrical tank containing liquefied propane is located close to an inhabited zone (Fig. 11.8). The tank has a volume of 82 m3 and is connected to the loading point by a pipe with a diameter of 2v and a length of 40 m; this pipe is fitted with an automatic excess flow rate valve which interrupts the flow when the flow rate reaches 3.5 kg s21. The pipe that connects the tank with the distribution system is also fitted with a similar valve. While loading the tank another 2v pipe (Lpipe 5 40 m) transports the propane gas back to the tank car. The road tanker has a volume of 20 m3 and is connected to the loading pipe through a flexible duct with a diameter of 2.5v and l 5 1.6 m. Loading operations are performed during (Continued)

456 Chapter 11 Example 11.4 (Continued)

Figure 11.8 Schematic representation of the LPG storage unit. Table 11.4: Wind rose. j 1 2 3 4 5 6 7 8 9 10 11 12

Wind Direction

Angle

Probability

N

0 30 60 90 120 150 180 210 240 270 300 330

5.7 8.0 8.8 8.5 8.5 8.6 8.5 11.1 11.6 9.9 5.5 5.2

E

S

W

N 12

8 4

W

0

E

S

(Continued)

Quantitative Risk Analysis 457 Example 11.4 (Continued) 87 hours year21 and a highly-trained operator is always present. The propane tank is protected from flame impingement by a water spray system. In winter conditions (90 days per year) an evaporating unit is used to evaporate the liquefied propane. The pipe connecting the tank with this unit is 40 m long and has a diameter of 2v. Average atmospheric data: P0 5 1.013 bar; ambient temperature 5 25 C; relative humidity 5 60%; two wind velocities must be considered: 2 m s21 and 5 m s21; wind direction: see wind rose (Table 11.4); atmospheric stability class: D (uw 5 5 m s21) and F (uw 5 2 m s21); surface roughness length 5 0.1 m. Identify the diverse initiating events and determine their frequencies. Determine the diverse accident sequences, calculate the frequency of the different accident scenarios, estimate the effects of the most significant accidents and establish the corresponding IR contours [12]. Solution

11.6.1 Estimation of the Frequencies of Initiating Events Table 11.5 gives descriptions of the initiating events considered. The generic frequencies were taken from a reference book [4]. The loading time per year was taken into account for Events 1
5. Events 7 and 8 can occur only over 90 days per year. The frequency of Events 3
5 and 7
9 was estimated taking into account the length of the corresponding pipes. We now develop the corresponding event trees to establish the different sequences from the different initiating events to the final accident scenarios. Table 11.5: Initiating events and their respective estimated frequencies.a Event 1

2

3

Description LPG release due to full-bore rupture of road tanker flexible pipe LPG release due to partial rupture of road tanker flexible pipe LPG release due to full-bore rupture of the pipe connecting the loading point with the tank

Frequency Estimation 26

Frequency

21

f 5 3.48  1024 year21

f 5 4  1025 h21  87 h year21

f 5 3.48  1023 year21

f 5 4  10

23

f 5 1U10

21

h

 87 h year

21

km

 year

21

87 h year21 8760 h year21



f 5 9.93  1026 km21 year21 f 5 3.97  1027 year21

458 Chapter 11 Table 11.5: (Continued) Event

23

Frequency Estimation   87 h year21 km21 year21 8760 h year21

4

LPG release due to partial rupture of the pipe connecting the loading point with the tank

f 5 5U10

5

Release of propane (gas) due to full-bore rupture of the pipe connecting the top of the tank with road tanker Release of propane (gas) through the safety relief valve LPG release due to full-bore rupture of the pipe connecting the tank with the evaporators LPG release due to partial rupture of the pipe connecting the tank with the evaporators Release of propane (gas) due to full-bore rupture of the pipe connecting the storage tank with the distribution system

f 5 6U1023 km21 year21

6

7

8

9

a

Description



87 h 8760 h year21



f 5 2  1025 year21 f 5 1U1023 km21 year21

Frequency f 5 4.97  1025 km21 year21 f 5 2  1026 year21

f 5 5.96  1025 km21 year21 f 5 2.38  1026 year21

f 5 2  1025 year21   ð90U24Þ h year21 8760 h year21

f 5 5U1023 km21 year21

f 5 2.47  1024 km21 year21 f 5 9.88  1026 year21

  ð90U24Þ h year21 f 5 1.23  1023 km21 year21 8760 h year21 f 5 4.93  1025 year21

f 5 6  1023 km21 year21

f 5 2.4  1024 year21

Frequencies taken from Table 9.2.

11.6.2 Event Trees of the Diverse Initiating Events Initiating event 1. Full-bore rupture of the flexible pipe. The first safety measure is the excess flow rate valve, which would stop the release. The second safety measure if the valve fails is for the operator to close the propane exit valve manually to stop the release. If we take into account the position of the flexible pipe and its distance from the tank and the tank car, we obtain a probability of 8% (which corresponds to an angle of 30 on a horizontal plane, required for the jet fire that affects the tank) for the storage tank (which is also protected by a water spray system) and 50% for the tank car due to its proximity to the pipe. The different sequences can be seen in the event tree (Fig. 11.9).

Quantitative Risk Analysis 459 Initiating event

Failure of excess flow rate

Immediate ignition

Flames Failure of Flames Operator Delayed Flame front impinge on water impinge on failure ignition acceleration tank spray system road tanker

Yes P4=0.083

Yes P5=0.05 No

Yes P2=0.5

No P4=0.917

Jet fire Yes P6=0.5

Road tanker BLEVE

No P6=0.5

Jet fire

No P3=0.8

No outcome Yes P9=0.01 Yes P8=0.5 No P9=0.99

Yes P7=0.2

Full-bore rupture No P2=0.5

f = 3.48 10–4y–1

Tank BLEVE

P5=0.95

Yes P3=0.2

Yes P1=0.05

Accidental scenario

No P8=0.5 No P7=0.8

Flash fire + VCE Flash fire No outcome No outcome

No P1=0.95

No outcome

Figure 11.9 Event tree and accident scenarios, initiating event 1 (full-bore rupture of the flexible pipe). Table 11.6: Frequencies of the accident scenarios associated with initiating event 1. Accident Scenario Jet fire Flash fire VCE Road tanker BLEVE Tank BLEVE

Frequency Estimation 24

f 5 (3.48  10  0.05  0.5  0.2  0.08  0.95) 1 (3.48  1024  0.05  0.5  0.2  0.92  0.5) f 5 (3.48  1024  0.05  0.5  0.2  0.5  0.01) 1 (3.48  1024  0.05  0.5  0.2  0.5  0.99) This frequency has not been estimated as significant peak pressures would not be reached f 5 3.48  1024  0.05  0.5  0.2  0.92  0.5 f 5 3.48  1024  0.05  0.5  0.2  0.08  0.05

Frequency f 5 9.15  1027 year21 f 5 8.7  1027 year21

f 5 8  1027 year21 f 5 6  1029 year21

The frequency of each accident scenario can be calculated according to the different sequences. Table 11.6 shows the corresponding values. Initiating event 2. Partial rupture of the flexible pipe. The release flow rate would be much lower—close to the unloading flow rate in normal operation—and the excess flow valve would not be closed. The resulting jet fire would be smaller and would not reach the storage tank. The probability that the tank car will be affected by the jet fire is kept as 0.5. Fig. 11.10 shows the corresponding event tree. The possibility of a blast wave due to the explosion of a flammable vapor cloud has not been considered, as the minimum amount of flammable mixture required to produce blast would not be reached.

460 Chapter 11 Initiating event

Immediate ignition

Flames Failure of Flames Operator Delayed Flame front impinge on water impinge on failure ignition acceleration tank spray system road tanker

Yes P4=0 Yes P3=0.2 Yes P2=0.2

No P4=1

Yes P5=0.05 No P5=0.95

No outcome Jet fire Yes P6=0.5

Road tanker BLEVE

No P6=0.5

Jet fire

No P3=0.8

Partial rupture

Accidental scenario

No outcome Yes P9=0 Yes P8=0.5 No P9=1

f = 3.48 10–3y–1 Yes P7=0.2 No P2=0.8

No P8=0.8 No P7=0.8

No outcome Flash fire No outcome No outcome

Figure 11.10 Event tree and accident scenarios for initiating event 2 (road tanker: partial rupture of the flexible pipe). Table 11.7: Frequencies of the accident scenarios associated with initiating event 2. Accident Scenario

Frequency Estimation

Frequency

f 5 3.48  10  0.2  0.2  1  0.5 f 5 6.96  1025 year21 f 5 3.48  1023  0.8  0.2  0.2  1 f 5 1.11  1024 year21 This frequency has not been estimated as it is considered that the minimum amount of flammable mixture required to produce blast would not be reached Road tanker BLEVE f 5 3.48  1023  0.2  0.2  1  0.5 f 5 6.96  1025 year21 Jet fire Flash fire VCE

23

Table 11.7 shows the estimated frequencies for the different accident scenarios. The probability of blast wave for VCE has been considered negligible. Initiating event 3. Full-bore rupture of the pipe connecting the loading point with the storage tank. The excess flow rate valve would stop the release. In order for a BLEVE to occur it would be necessary for the jet fire to impinge on the tank or the road tanker. A probability of 0.15 is assumed for the storage tank, taking into account the length of the connecting pipe and the angle of the jet that would cause it to affect the tank (35 ). In the case of the road tanker, a length of 13 m and an angle of 23 give a probability of 0.02. Fig. 11.11 shows the corresponding event tree. The estimated frequencies can be seen in Table 11.8

Quantitative Risk Analysis 461 Initiating event

Failure of excess flow valve

Immediate Operator Flames impinge Failure of water Flames impinge ignition failure on tank spray system on road tanker

Yes P4=0.15

Delayed ignition

Flame front Accidental acceleration scenario

Yes P5=0.05 No

Tank BLEVE Jet fire

P5=0.95

Yes P3=0.2 Yes P2=0.2

No P4=0.85

Yes P6=0.02

Road tanker BLEVE

No P6=0.98

Jet fire

No P3=0.8

Yes P1=0.05

No outcome

Yes P8=0.2

Yes

P7=0.2 Full-bore rupture

No

f = 3.97 10–7y–1

P2=0.8

No P8=0.8 No P7=0.8

Yes P9=0 No P9=1

No outcome Flash fire No outcome No outcome

No

No outcome

P1=0.95

Figure 11.11 Event tree and accident scenarios for initiating event 3 (full-bore rupture of the pipe connecting the loading point with the storage tank). Table 11.8: Frequencies of the accident scenarios associated with initiating event 3. Accident Scenario Jet fire Flash fire VCE

Road tanker BLEVE Tank BLEVE

Frequency Estimation

Frequency

f 5 (3.97  10  0.05  0.2  0.2  0.15  0.95) 1(3.97  1027  0.05  0.2  0.2  0.85  0.98) f 5 3.97  1027  0.05  0.8  0.2  0.2  1 This frequency has not been estimated as it is considered that the minimum amount of flammable mixture required to produce blast would not be reached f 5 3.97  1027  0.05  0.2  0.2  0.85  0.02 f 5 3.97  1027  0.05  0.2  0.2  0.15  0.05

f 5 7.75  10210 year21

27

f 5 6.35  10210 year21

f 5 1.35  10211 year21 f 5 6  10212 year21

Initiating event 4. Partial rupture of the pipe connecting the loading point with the storage tank. In this case the release flow rate would be similar to the normal unloading release from the road tanker. Therefore, only the operator would be able to stop the flow. The rest of the sequences are similar to those for the previous event trees (see Fig. 11.12). Table 11.9 shows the estimated frequencies. Initiating event 5. Full-bore rupture of the pipe connecting the top of the tank with the road tanker. The rupture originates a release of propane (gas). In this case the operator should

462 Chapter 11 Initiating event

Immediate ignition

Operator failure

Flames impinge Failure of water Flames impinge on tank spray system on road tanker

Yes P4=0.15 Yes P3=0.2 Yes P2=0.2

No P4=0.85

Delayed ignition

Flame front acceleration

Yes P5=0.05 No P5=0.95

Tank BLEVE Jet fire Yes P6=0.02

Road tanker BLEVE

No P6=0.98

Jet fire

No P3=0.8

Partial rupture

Accidental scenario

No outcome

f = 2 10–6y–1

Yes P8=0.2

Yes P7=0.2 No P2=0.8

Yes P9=0 No P9=1

No P8=0.8 No P7=0.8

No outcome Flash fire No outcome No outcome

Figure 11.12 Event tree and accident scenarios for initiating event 4 (partial rupture of the pipe connecting the loading point with the storage tank).

Table 11.9: Frequencies of the accident scenarios associated with initiating event 4. Accident Scenario Jet fire Flash fire VCE

Road tanker BLEVE Tank BLEVE

Frequency Estimation

Frequency

f 5 (2  10  0.2  0.2  0.15  0.95) 1(2  1026  0.2  0.2  0.85  0.98) f 5 2  1026  0.8  0.2  0.1  1 This frequency has not been estimated as it is considered that the minimum amount of flammable mixture required to produce blast is not reached f 5 2  1026  0.2  0.2  0.85  0.02 f 5 2  1026  0.2  0.2  0.15  0.05

f 5 7.8  1028 year21

26

f 5 3.2  1028 year21

f 5 1.36  1029 year21 f 5 6  10210 year21

close the valve. The lay-out of the pipe is the same as in the previous cases, so the same probabilities and assumptions apply (Fig. 11.13 and Table 11.10): jet fire flames can impinge on the storage tank or on the road tanker. Initiating event 6. Release of propane gas through the safety relief valve. The frequency of the initiating event is taken from Table 9.2. As the relief valve discharges vertically and is located 1 m above the tank top, it is assumed that there would be no significant effects on either the tank or the tank car in the event of ignition (Fig. 11.14 and Table 11.11): no significant outcomes would occur.

Quantitative Risk Analysis 463 Immediate ignition

Initiating event

Operator failure

Flames impinge on tank

Yes P4=0.15 Yes P3=0.2 Yes P2=0.2

Failure of water spray system Yes P5=0.05 No P5=0.95

No P4=0.85

Full-bore rupture f = 2.38 10–6y–1

Flames impinge Accidental scenario on road tanker Tank BLEVE Jet fire Yes P6=0.02

Road tanker BLEVE

No P6=0.98

Jet fire

No P3=0.8

No outcome

No P2=0.8

No outcome

Figure 11.13 Event tree and accident scenarios for initiating event 5 (full-bore rupture of the pipe connecting the top of the tank with the road tanker).

Table 11.10: Frequencies of the accident scenarios associated with initiating event 5. Accident Scenario Jet fire Road tanker BLEVE Tank BLEVE

Initiating event

Frequency Estimation f 5 (2.38  1026  0.2  0.2  0.15  0.95) 1(2.28  1026  0.2  0.2  0.85  0.98) f 5 2.38  1026  0.2  0.2  0.85  0.02 f 5 2.38  1026  0.2  0.2  0.15  0.05

Immediate ignition

Flames impinge on tank

No P4=1

Opening of PSV f = 2 10–5y–1 No P2=0.8

f 5 1.62  1029 year21 f 5 7.14  10210 year21

Flames impinge on road tanker

Yes P4=0 Yes P2=0.2

Frequency f 5 9.29  1028 year21

Accidental scenario

No outcome Yes P6=0

No outcome

No P6=1

Jet fire

No outcome

Figure 11.14 Event tree and accident scenarios for initiating event 6 (release of propane gas through the safety relief valve).

464 Chapter 11 Table 11.11: Frequencies of the accident scenarios associated with initiating event 6. Accident Scenario

Frequency Estimation 25

f 5 2  10

Jet fire

Initiating event

Failure of Failure of Immediate excess automatic ignition flow valve valve

Yes P3=0.05 No P4=0.85

Yes P7=0.05

Full-bore rupture No P2=0.8

Accidental scenario

Tank BLEVE Jet fire Yes P6=0.02

Road tanker BLEVE

No P6=0.98

Jet fire No output Yes Yes P9=0 P8=0.2 No P9=1 No P8=0.8

No P7=0.95 No P1=0.95

Yes P5=0.05 No P5=0.95

No P3=0.95

Yes P1=0.05

f = 9.88 10–6y–1

f 5 4  1026 year21

 0.2  1  1

Flames Failure of Flames Delayed Flame front impinge on water impinge on ignition acceleration tank spray system road tanker

Yes P4=0.15

Yes P2=0.2

Frequency

No output Flash fire

No output No output No output

Figure 11.15 Event tree and accident scenarios for initiating event 7 (full-bore rupture of the pipe connecting the tank with the evaporators).

Initiating event 7. Full-bore rupture of the pipe connecting the tank with the evaporators. In this case the excess flow-rate valve should close automatically. This event may occur while the operator is away from the plant. The equipment is fitted with a set of automatic valves that stops the flow of LPG from the storage tank in the event of a fire: the sequences leading to the different accident scenarios therefore depend on the failure of this automatic shut-off system. The assumptions and probabilities are essentially the same as those applied in the previous cases (Fig. 11.15 and Table 11.12). Initiating event 8. Partial rupture of the pipe connecting the tank with the evaporators. In this case the set of automatic valves installed in the storage tank exit pipe may be activated (depending on the release flow rate), which stops the flow. The rest of the sequences and probabilities are similar to those for the previous case (Fig. 11.16 and Table 11.13). The possibility of a storage tank BLEVE depends on the failure of the water spray system (probability of failure of this system: see Section 6.2).

Quantitative Risk Analysis 465 Table 11.12: Frequencies of the accident scenarios associated with initiating event 7. Accident Scenario Jet fire Flash fire VCE

Road tanker BLEVE Tank BLEVE

Initiating event

Frequency Estimation

Frequency

f 5 (9.88  10  0.05  0.2  0.05  0.15  0.95) 1 (9.88  1026  0.05  0.2  0.05  0.85  0.98) f 5 9.88  1026  0.05  0.8  0.05  0.2  1 This frequency has not been estimated as it is considered that the minimum amount of flammable mixture required to produce blast is not reached f 5 9.88  1026  0.05  0.2  0.05  0.85  0.02 f 5 9.88  1026  0.05  0.2  0.05  0.15  0.05

f 5 4.9  10210 year21

26

Immediate ignition

Failure of automatic valves

Flames impinge on tank

Yes P4=0.15

Yes P2=0.2

Yes P3=0.05

No P4=0.85

Flames Failure of water impinge on spray system road tanker

Delayed ignition

f 5 8.4  10211 year21 f 5 3.7  10211 year21

Flame front acceleration

Yes P5=0.05 No P5=0.95

Accidental scenario

Tank BLEVE Jet fire Yes P6=0.02

Road tanker BLEVE

No P6=0.98

Jet fire

No P3=0.95

Partial rupture

f 5 3.9  1029 year21

No outcome

f =4.93 10–5y–1

Yes P8=0.2

Yes P7=0.05 No

No P8=0.8

P2=0.8 No

Yes P9=0 No P9=1

No outcome Flash fire No outcome No outcome

Figure 11.16 Event tree and accident scenarios for initiating event 8 (partial rupture of the pipe connecting the tank with the evaporators). Table 11.13: Frequencies of the accident scenarios associated with initiating event 8. Accident Scenario

Frequency Estimation

Frequency

f 5 (4.93  1025  0.2  0.05  0.15  0.95) f 5 4.8  1027 year21 25 1(4.93  10  0.2  0.05  0.85  0.98) Flash fire f 5 4.93  1025  0.8  0.05  0.2  1 f 5 3.9  1027 year21 VCE This frequency has not been estimated as it is considered that the minimum amount of flammable mixture required to produce blast is not reached Road tanker BLEVE f 5 4.93  1025  0.2  0.05  0.85  0.02 f 5 8.38  1029 year21 Tank BLEVE f 5 4.93  1025  0.2  0.05  0.15  0.05 f 5 3.7  1029 year21 Jet fire

466 Chapter 11 Initiating event

Immediate ignition

Failure of automatic valves

Flames impinge on tank

Yes P4=0.15

Yes P2=0.2 Full-bore rupture

Yes P3=0.05

Failure of water spray system Yes P5=0.05 No P5=0.95

No P4=0.85

No P3=0.95

f = 2.4 10–4y–1

Flames impinge Accidental scenario on road tanker Tank BLEVE Jet fire Yes P6=0.02

Road tanker BLEVE

No P6=0.98

Jet fire No outcome

No

No outcome

P2=0.8

Figure 11.17 Event tree and accident scenarios for initiating event 9 (full-bore rupture of the pipe connecting the tank with the distribution system). Table 11.14: Frequencies of the accident scenarios associated with initiating event 9. Accident Scenario Jet fire Road tanker BLEVE Tank BLEVE

Frequency Estimation 24

f 5 (2.4  10  0.2  0.05  0.15  0.95) 1(2.4  1024  0.2  0.05  0.85  0.98) f 5 2.4  1024  0.2  0.05  0.85  0.02 f 5 2.4  1024  0.2  0.05  0.15  0.05

Frequency f 5 2.3  1026 year21 f 5 4.08  1028 year21 f 5 1.8  1028 year21

Initiating event 9. Full-bore rupture of the pipe connecting the tank with the distribution system (release of gas phase). In the event of a full-bore rupture of the pipe connecting the storage tank with the distribution piping system, the different sequences depend on the action or failure of the automatic valves installed to stop the propane flow in the event of a fire. The final sequences are similar to those in the previous event trees (Fig. 11.17, Table 11.14).

11.6.3 Effects of the Different Accident Scenarios We will now calculate the effects of the most severe accident scenarios considered: storage tank BLEVE/fireball, road tanker BLEVE/fireball, release of propane creating a flammable cloud (flash fire), and jet fire. Nomenclature: see the respective chapters. 11.6.3.1 Initiating Event 1. Release of Propane (Liquid) due to the Full-Bore Rupture of the Flexible Pipe Connecting the Road Tanker with the Storage Tank Road tanker filling degree: 10%; road tanker volume: 20 m3; dpipe 5 0.0635 m; ambient temperature 5 25 C; wind speed 5 5 m s21; stability 5 class D; ground roughness 5 10 cm;

Quantitative Risk Analysis 467 relative humidity 5 60%; LFLpropane 5 2.1%; ρpropane, liquid 5 553 kg m23; ρpropane, gas, Tb 5 2.32 kg m23; propane boiling temperature at atmospheric pressure 5 242 C. The maximum distance reached by c 5 LFL will be calculated by applying the Britter
McQuaid model. Due to the storage conditions, liquid propane undergoes a flash vaporization and is released as a two-phase flow. If it was released only as a gas the mass flow rate would be approximately 7.6 kg s21. The flow rate in increased by 45% to allow for the two-phase flow; therefore, we obtain an approximate value of 11 kg s21. v0 5

11 5 4:74 m3 s21 2:32

2:32 2 1:2 9:16 m s21 1:2   4:74 1=2 D5 5 0:974 m 5

g0 5

9:16  4:74 5 0:357 . 0:15 . dense gas 53  0:974 5 ð1:5  60Þ $ 2:5 x Therefore, the release can be considered continuous up to x 5 180 m. c5

0:021

 5 0:01635 m3 m23 298 0:021 1 ð1 2 0:021Þ 231 

 1=5 9:162  4:74 5 0:425 55 

x

x 1=2 5 0:97 4:74 5 c 5 0:01635 c0

From Fig. 7.19, x 5 200; x 5 194 m 0:97

468 Chapter 11 At this distance the release cannot be considered continuous. If the calculation is repeated for an instantaneous release: V0 5 4:74 m3 

9:16  4:741=3 52

1=2 5 0:784

x x x ffiffiffiffiffiffiffiffiffi 5 p ; 5 105; x 5 176 m 3 1:68 1:68 4:74 In both cases, this distance seems too conservative. The simulation with standard computer codes gives x  50 m. Therefore, we assume an intermediate value of x 5 100 m for illustrative purposes. Furthermore, the blast would be negligible due to the small amount released. 11.6.3.2 Initiating Event 9. Release of Propane (gas) Due To the Full-Bore Rupture of the Pipe Connecting the Tank with the Distribution System Tank filling degree: 70%; tank volume 5 115 m3; Ttank 5 25 C; Ptank 5 9.5 bar; Lpipe 5 20 m; dpipe 5 0.0508 m; ε 5 45  1026 m. 11.6.3.2.1 Estimation of the Initial Release Flow Rate

Estimated pressure at a point just in front of the pipe opening: 9.3 bar. A value of fF 5 0.0048 is assumed. Applying Eq. (2.34): 1 0  ð1:15 2 1Þ 2     Macont 2 11 C 1:15 1 1 B 1 4U0:0048U20 2 C2 ln B 2 1 1 1:15 50 A @ ð1:15 1 1Þ Ma2cont 2 Ma2cont 0:0508 By trial and error, Macont 5 0.28. Therefore, by applying Eq. (2.29): Ycont 5 1 1

1:15 2 1 0:282 5 1:00588 2

Quantitative Risk Analysis 469 From Eq. (2.33): Tp 2  1:00588 5 1:15 1 1 298 Tp 5 279 K Mass flow rate through the opening (Eq. (2.19)): vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  1:1511 u 1:1521  π 0:05082  2 44:1 t 5 1 9:3  10 1 1:15 mhole 5 5 5:25 kg s21 1:1511 4 279 U 8:314  103 Mass flow rate through the pipe (Eq. (2.24)) (ρcont 5 17.1 kg m23): vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 11ffi u 0 111:15     u 1:15  1:15 u @  @ 9:3 2 1AA u2 2 9:5  105 17:1 111:15 9:5 2u π 0:0508 u   u 5 0:54 kg s21 mpipe 5 t 20 4 4  0:0048 0:0508 A new trial is required. The following table shows the results of the calculation procedure: Pp (bar)

mhole (kg s21)

mpipe (kg s21)

5.25 4.51 3.95 2.82 2.63

0.54 1.61 2.03 2.57 2.63

9.3 8 7 5 4.7

Therefore, m 5 2.63 kg s21. 11.6.3.2.2 Calculation of the Jet Fire Size

   1:1521 1:15 1:013125 5 222 K Tj 5 ð324Þ 9:5 



 1:15 1:1521 2 Por 5 9:5 5 5:46 bar 1:1511

470 Chapter 11 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  1:1521 u 5:46 1:15 u uð1:15 1 1Þ 22 t 1:013 5 2:126 Mj 5 ð1:15 2 1Þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1:15  8314 U222 uj 5 2:126 5 467 m s21 44:1 For choked flow: 273 5 2:4 kg m23 222:5 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4  2:63 dj 5 5 0:05466 π  467U2:4  1=2 2:4 5 0:0789 m ds 5 0:05466 1:2 ρj 5 1:969

cst-mass 5 0:06 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2:85 2=3 3 9:81  0:0789 5=3 2=3 0:024 Y 1 0:2 Y 2 50 0:06 4672 By trial and error, Y 5 290 Lbo 5 290  0:0789 5 22:9 m An angle of 45 is assumed between the hole axis and the wind vector.    Lb 5 22:9 0:51 e20:45 1 0:49 1 2 6:07  1023 ð45 2 90Þ 5 16:3 m Rw 5

5 5 0:0107 467

  s 5 16:3 0:185 e2200:0107 1 0:015 5 2:6 m C0 5 1000Ue2100U0:0107 1 0:8 5 343  1=3 9:81 5 0:0152 Rids 5 0:0789 0:07892  4672 " # " #  1=2   1:2 1 W1 5 0:0789 13:5 e260:0162 1 1:5 1 2 1 2 e2700:01513430:0107 5 1:07 m 2:4 15

Quantitative Risk Analysis 471    W2 5 16:3 0:18 e21:50:0107 1 0:31 1 2 0:47 e2250:0107 5 5:05 m 

9:81 RiLb0 5 22:9 0:07892  4672

1=3 5 4:43

  0:0107 α 5 ð45 2 90Þ 1 2 e225:60:0107 1 8000 5 9 4:43 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L 5 16:32 2 2:62 sin2 9 2 2:6 cos 9 5 13:7 m The point source model can be applied to establish the safe distance (corresponding to I 5 1 kW m22):   0:21 e20:00323467 1 0:11 2:63  46000  0:81 15 4πd 2 Therefore, the intensity of 1 kW m22 is found at a horizontal distance of 49 m from the release point. 11.6.3.2.3 Estimation of the Thermal Effects of the Road Tanker BLEVE/Fireball

Vessel volume 5 20 m3; filling degree: 50%; ρpropane, 25 C 5 500 kg m23; relative humidity 5 60%. The propane mass is 20U0:5U500 5 5000 kg Fireball diameter (Eq. (3.95)): D 5 5:8U50001=3 5 99 m Duration (Eq. (3.93)): t 5 0:9U50000:25 5 7:5 seconds Height at which the fireball center is located: H 5 0:75  99 5 74 m Radiant heat fraction (Eq. (3.99)):  0:32 ηrad 5 0:00325U 9:5U105 5 0:266

472 Chapter 11 Emissive power (Eq. (3.100)): E5

0:266U5000U46;000 5 260 kW m22 π 992 U7:5

The partial pressure of water in the atmosphere is calculated by using Eqs. (3.18) and (3.19): Pw 5 1857 Pa. The intensity of the thermal radiation at different distances is calculated by applying the solid flame model, e.g., for a distance x 5 150 m: Distance between the flame and the target: d 5 118 m. Atmospheric transmissivity: τ 5 2:85 ð1857  118Þ20:12 5 0:65 View factor: F5

 4

992 99 1118 2

2 5 0:087

I 5 0:65  0:087  260 5 14:8 kW m22 And on a vertical surface: Iv 5 14:8 

150 5 13:2 kW m22 167

The following table shows the values of Iv as a function of the distance from the initial position of the tank car. x (m) 50 70 80 100 120 150

Iv (kW m22)

x (m)

Iv (kW m22)

33.0 30.2 27.8 22.8 18.3 13.3

200 250 300 400 500 585

8.2 5.4 3.8 2.1 1.3 1.0

11.6.3.2.4 Estimation of the Peak Overpressure of the Road Tanker BLEVE

The value of ΔP is calculated by applying the concept of superheating energy (Eq. (5.27)). The gas expansion is assumed to be an irreversible process, in which approximately 5% of

Quantitative Risk Analysis 473 SE is devoted to creating overpressure. Thus, at a distance of 50 m from the initial tank car location: Enthalpies of liquid propane: at 9.5 bar, 25 C, hl 5 265.3 kJ kg21; at 1.013 bar, 231 C, hlo 5 100 kJ kg21. SE 5 265:3 2 100 5 165:3 kJ kg21 For the total mass of propane: 165:3 kJ kg21 U5000 kg 5 826;500 kJ Energy converted into overpressure (5%): 826;500 kJ  0:05 5 41;350 kJ   WTNT 5 41;350U 0:214U1023 5 8:8 kg At a distance of 50 m, dn 5 24 m kg21/3; from Fig. 4.4, ΔP  0.04 bar. This overpressure does not pose a danger to people. The typical threshold value of ΔP for glass breakage (0.01 bar) is found at 160 m. 11.6.3.2.5 Estimation of the Thermal Effects of the Storage Tank BLEVE/Fireball

Vessel volume 5 82 m3; filling degree: 70%; ρpropane, 25 C 5 500 kg m23; relative humidity 5 60%. In the worst-case scenario the BLEVE occurs very quickly after flame impingement. Therefore, the propane mass is 82  0:7  500 5 28;700 kg Fireball diameter: D 5 5:8  28;7001=3 5 178 m Duration: t 5 0:9  28;7000:25 5 11:7 seconds Height at which the fireball center is located: H 5 0:75  178 5 133 m Radiant heat fraction: ηrad 5 0:266

474 Chapter 11 Emissive power: E5

0:266  28;700  46;000 5 300 kW m22 π 1782  11:7

The partial pressure of water in the atmosphere is Pw 5 1857 Pa. The intensity of the thermal radiation at different distances is calculated by applying the solid flame model for an example distance x 5 250 m. Distance between the flame and the target: d 5 194 m. Atmospheric transmissivity: τ 5 2:85 ð1857  194Þ20:12 5 0:614 View factor: F5

 4

1782

2 5 0:099 178 1194 2

Iv 5 0:614  0:099  300 U

250 5 16:1 kW m22 283

The following table shows the values of Iv as a function of the distance from the initial position of the tank car. x (m) 100 150 200 250 300

Iv (kW m22)

x (m)

Iv (kW m22)

35.4 23.4 21.6 16.1 12.1

400 500 600 700 950

7.3 4.8 3.1 2.4 1.0

11.6.3.2.6 Estimation of the Peak Overpressure for the Storage Tank BLEVE

Enthalpies of liquid propane: at 9.5 bar, 25  C, hl 5 265.3 kJ kg21; at 1.013 bar, 231 C, hlo 5 100 kJ kg21. SE 5 265:3 2 100 5 165:3 kJ kg21 For the total mass of propane, 165:3 kJ kg21  28;700 kg 5 4:752375  106 kJ

Quantitative Risk Analysis 475 Energy converted into overpressure (5%): 4:752375  106 kJU0:05 5 237;620 kJ   WTNT 5 237; 620U 0:214U1023 5 50:9 kg At a distance of 50 m, dn 5 13.5 m kg21/3; from Fig. 4.4, ΔP  0.1 bar. This overpressure does not pose a danger to people. The typical threshold value of ΔP for glass breakage (0.01 bar) is found at 300 m.

11.6.4 Calculation of the Individual Risk The IR will be calculated for a point located 100 m from the center of the plant in the direction j 5 3 (wind blowing from 240 ; see wind rose, Table 11.4). For practical purposes, all initiating events will be assumed to occur in the center of the installation. Meteorological data, probabilities: • • •

stability class D, PM 5 0.8 stability class F, PM 5 0.2 wind blowing from 240 , Pw 5 0.116.

The point is affected by the following accident scenarios: • • •

flash fire tank car BLEVE/fireball storage tank BLEVE/fireball

We will calculate the contribution of these accident scenarios to IR. 11.6.4.1 Flash Fire For the sake of simplicity, we consider that the flammable cloud reaches the point for both stability classes (although they would actually give two different values). Furthermore, we consider that the probability of death in the area covered by the flash fire is Pd 5 1 (see Chapter 8: Vulnerability, Section 4.1.3). Overall frequency taking into account the different initiating events (Tables 11.6
11.14): fflash fire 5 8:7  1027 1 1:11  1024 1 6:35  10210 1 3:2  1028 1 3:9  1029 1 3:9  1027 5 1:12  1024 year21 P 5 0:116  ð0:8 1 0:2Þ  1 5 0:116   ΔIRflash fire 5 1:12  1024  0:116 5 1:3  1025 fatalities year 21

476 Chapter 11 11.6.4.2 Road Tanker Fireball froad tanker fireball 5 8  1027 1 6:96  1025 1 1:35  10211 1 1:36  1029 1 1:62  1029 1 8:4  10211 1 8:38  1029 1 4:08 108 5 7:05  1025 year21 At x 5 100 m, I 5 22.8 kW m22 during 7.5 s

Y 5 2 36:38 1 2:56 ln 7:5  22;8004=3 5 3:03; 2:5% deaths; Pd 5 0:025

ΔIRroad tanker fireball 5 7:05  1025  0:025 5 1:76  1026 fatalities year21 11.6.4.3 Storage Tank Fireball froad tanker fireball 5 6  1029 1 6  10212 1 6  10210 1 7:14  10210 1 3:7  10211 1 3:7  1029 1 1:8  1028 5 2:9  1028 year21 At x 5 100 m, I 5 35.4 kW m22 during 11.7 s

Y 5 2 36:38 1 2:56 ln 11:7  35; 4004=3 5 5:67; 75% deaths; Pd 5 0:75   ΔIRstorage tank fireball 5 2:9  1028  0:75 5 2:18  1028 fatalities year21 Therefore, the IR at the selected point due to all the accident scenarios considered is: IR 5 1:3  1025 1 1:76  1026 1 2:18  1028 5 1:48  1025 fatalities year21 In order to determine the influence of the meteorological conditions we calculate the IR at a point located at the same distance from the initiation point but in the opposite direction (j 5 9): fflash fire 5 1:12U1024 year21 Pw 5 0:088; P 5 0:088  1  1 5 0:088   ΔIRflash fire 5 1:12  1024  0:088 5 9:86  1026 fatalities year 21 The IR caused by the two fireballs does not depend on the direction. Therefore, IR 5 9:86  1026 1 1:76  1026 1 2:18  1028 5 1:16  1025 fatalities year 21 Fig. 11.18 shows the iso-risk curves for this scenario. The influence of the flash fire is clear for short distances, while for larger distances the IR depends essentially on the fireballs effects, which are uniform in all directions.

Quantitative Risk Analysis 477

Figure 11.18 Individual risk curves.

11.7 Some Additional Criteria Often Applied in QRA In standard quantitative risk analyses various criteria, based on expert knowledge, are commonly applied in order to simplify them; see, for example, [4] or [13]. The most significant examples are included here.

11.7.1 Initiating Events that can be Neglected Initiating events with a frequency #1029 year21 are usually neglected. Initiating events for which the range of the 1% lethality corresponding to the most severe associated final accident, at the worst meteorological conditions, does not surpass the plant boundary.

11.7.2 Full Bore Rupture of a Pipe Connected to a Pump In case of full bore rupture of a pipe near the pump, assume the maximum release flow rate equal to 1.5 times the normal operation one. If the rupture occurs at a significant distance from the pump, the operation flow rate is assumed.

478 Chapter 11 Table 11.15: Duration of the release. Type of Valve Automatic

Remotely operated

Manually operated

Description

Time for Detection and Actuation (min)

The detection is completely automatic and specific The detection generates an automatic order to shut-off the valve No operator action is required The detection is completely automatic and specific The detection originates an alarm signal (in the plant or at the control room) The operator ratifies the signal, locates the valve switch and actuates it in the plant or in the control room The detection is completely automatic and specific The detection originates an alarm signal (in the plant or at the control room) The operator ratifies the signal, goes to the place, identifies the valve and closes it

2

10

30

11.7.3 Equipment Filling Degree Assume the maximum filling degree of equipment.

11.7.4 Duration of the Release The following times are assumed (Table 11.15).

11.7.5 Lethality Levels due to Overpressure The following values are often assumed [5]: For people onshore, outdoors and in the open: • •

0.35 bar: 15% lethality 0.5 bar: 50% lethality.

For people onshore, outdoors but in process units or adjacent to buildings: • •

0.35 bar: 30% lethality 0.5 bar: 100% lethality.

For people offshore, in modules affected by the explosion: •

0.25
0.3 bar: 100% lethality.

In standard QRA often an overall value of 100% lethality for ΔP $ 0.3 bar is also applied.

Quantitative Risk Analysis 479

11.7.6 Liquid Spills For liquid releases in unconfined surfaces on land, a pool with a depth of 10 mm and a maximum surface of 1500 m2 is assumed.

11.7.7 Vapor Cloud Explosion and Flash Fire If there is an unconfined flammable cloud with a mass ranging between the flammability limits equal or higher than 10,000 kg, the probability of explosion is assumed to be 0.4 and the probability of a flash fire is 0.6. If there is a flash fire, the lethality is considered to be 100% in the range of the Lower Flammability Limit.

11.7.8 Meteorological Data Data concerning stability class and wind velocity are usually grouped into a small number of representative sets. In [4], six representative sets are suggested. Often, two sets are used [13]: stability class D, 5 or 4 m s21, and stability class F, 1.5 or 2 m s21.

Nomenclature c D d da di dn dor ds E F f fF fi fN Fv go H hl hlo HR I IRav IRx,y IRx,y,i

concentration (% volume) fireball diameter (m) distance between the surface of the flames and the target (m) alert zone distance (m) intervention distance (m) scaled distance (m kg21/3) orifice or outlet diameter (m) effective orifice diameter (m) flame emissive power (kW m22) view factor (
) frequency (year21) Fanning friction factor (
) frequency of the accident scenario i (year21) frequency of all accident scenarios with N or more fatalities (year21) view factor, vertical surface (
) initial corrected gravity (m s22) height at which the fireball center is located (m) enthalpy of the liquid at temperature T (kJ kg21) enthalpy of the liquid at temperature T0 (kJ kg21) relative humidity of the atmosphere (%) intensity of the thermal radiation reaching a given target (kW m22) average individual risk (exposed population) (year21) total individual risk of fatality at the geographical location x, y (year21) individual risk of fatality at the geographical location x, y from the accidental scenario i (year21)

480 Chapter 11 L LBv Lpipe M m Ma Mw Ni Rw P P PFi px,y P0 Pw ΔP Re s T t Ta Tcont T0 Tj Tp usound uw v0 WTNT x Y α αβ ε ηrad ρa ρf
a ρj τ

length of the visible flame (m) vertical distance between the gas outlet and the flame tip (m) pipe length (m) mass of substance (kg) mass flow rate (kg s21) Mach number (5 u us21) (
) molecular weight (kg kmole21) number of fatalities from each accident scenario (
) ratio between wind velocity and jet velocity at the gas outlet (
) pressure (N m22 or bar) probability (
) probability that the accidental scenario i results in a fatality at location x, y (
) number of people at location x, y (
) atmospheric pressure (N m22) partial pressure of water in the atmosphere (N m22) peak overpressure (bar) Reynolds number (
) lift-off distance (m) temperature (K) fireball duration (s) ambient temperature (K) temperature inside the container (K) boiling temperature at atmospheric pressure (K) jet temperature at the gas outlet (K) temperature of the gas at a given point of the pipe (K) speed of sound in a given gas (m s21) wind speed (m s21) initial plume flow rate (m3 s21) TNT equivalent mass (kg) horizontal distance between the center of the fireball and the target (Fig. 3.14) (m) probit variable (
) tilt angle of a jet fire ( ) angle between the axis of the orifice and the line joining the center of the orifice and the tip of the flame ( ) pipe roughness (m) radiant heat fraction (
) air density (kg m23) density of the fuel
air mixture (kg m23) density of gas in the outlet (kg 23) atmospheric transmissivity (
)

References [1] Health and Safety Executive. Canvey: An Investigation of Potential Hazards from operations in the Canvey Island/Thurrock Area, HM Stationery Office, London, 1978. [2] Health and Safety Executive. Canvey: A Second Report, A Review of the Potential Hazard from Operations in the Canvey Island/Thurrock Area Three Years after Publication of the Canvey Report, HM Stationery Office, London, 1981.

Quantitative Risk Analysis 481 [3] Rijnmond Public Authority, A Risk Analysis of 6 Potentially Hazardous Industrial Objects in the Rijnmond Area-A Pilot Study, D. Reidel, Dordrecht, 1982. [4] Guidelines for quantitative risk assessment (Purple Book), CPR 18E, Ministerie van Verker en Waterstaat, Voorburg, 2005. [5] Reference Manual Bevi Risk Assessments, version 3.2, National Institute of Public Health and the Enviro (RIVM), Bilthoven, 2009. [6] Center for Chemical Process Safety, Guidelines for Chemical Process Quantitative Risk Analysis, second ed., AIChE, New York, 2000. [7] A. Ronza, L. La´zaro, S. Carol, J. Casal, J. Loss. Prev. Process Ind. 22 (2009) 639
648. [8] M. Considine, The Assessment of Individual and Societal Risks, SRD Report R-310, Safety and Reliability Directorate, UK Atomic Energy Authority, Arrington, 1984. [9] C.M. Pietersen, B.F.P. Van het Veld, J. Loss Prev. Process Ind. 5 (1992) 60. [10] OGP, Risk Assessment data directory, Report No. 434-14.1, 2010. [11] D. C. Hendershot, A Simple Problem to Explain and Clarify the principles of Risk Calculation, 1997, , http://home.att.net/-d.c.hendershot/papers/pdfs/riskland.pdf . (consulted 19/V/2007). [12] J. A. Vı´lchez. Personal communication. [13] Generalitat de Catalunya, Instruccio´ 14/2008 SIE, Criteris per a la realitzacio´ de les ana`lisis quantitatives de risc a Catalunya, Barcelona, 2008.