1 INTRODUCTION

If safety measures for self-rescue can not be as-sessed within a quantitative risk analysis (QRA), the risk judgement system does not motivate companies or local authorities to take measures, because their effects are not visible in a state-of-the-art risk as-sessment. In most quantitative risk analysis methods, persons present in the hazardous area are assumed to be exposed for a fixed amount of time. Assumptions for fixed exposure times are 30 minutes for a toxic exposure and 20 seconds for exposure to heat radia-tion. Furthermore, persons are assumed to stay on the same place. The reality is different: in case of an emergency, every person capable of escape will try to rescue himself. In case of a toxic release it is pos-sible that a safe place (for example inside a building) is reached within the prescribed 30 minutes. On the other hand, in case of fire in crowded places, it can be expected that people are unable to escape within 20 seconds. Examples of methods are the Dutch probabilistic QRA methods for transport of danger-ous goods and for stationary installations (Uijt de Haag 2006). In QRA calculations where self-rescue is very important, for instance in tunnel safety stud-ies, extensive calculations with evacuation models are performed. Subsequently the output of the evacuation models is used in the QRA, the evacua-tion model is not integrated within the QRA.

The model described in this article provides a so-lution between evacuation modelling, which might be too time-consuming and state-of-the-art QRA-calculations, which have insufficient detail to show the effect of safety measures. The model can be in-tegrated in a quantitative risk analysis method,

therewith enabling to account for self-rescue and to show the effect of safety measures by running a sin-gle QRA model. The model is especially suitable for QRA’s involving risks to densely populated areas, such as railway stations, stadiums, and offices as well as for industrial plants and their inhabited sur-roundings.

2 MODEL OUTLINE

In order to judge the effect of self-rescue improving measures, a model has been developed to quantify the effect of self-rescue, depending on exposure to fire or toxic chemicals. The model distinguishes heat radiation, smoke and several types of toxic chemi-cals and quantifies their effect on the walking veloc-ity and exposure duration (see Figure 1).

Figure 1. Self-rescue in quantitative risk analysis

### Self-rescue in quantitative risk analysis

### I.J.M. Trijssenaar- Buhre & I.M.E. Raben & T. Wiersma & S.I. Wijnant

*TNO, Apeldoorn, The Netherlands*

ABSTRACT: In quantitative risk analysis (QRA) methods, the damage of toxic and fire effects to persons is determined using a fixed exposure time. The model described in this paper enables to include self rescue in QRA methods. The model can be used 1) for calculations of a more realistic exposure time, 2) to determine the number of persons incapable of self-rescue, which is important information for the rescue services 3) to determine the effect of safety measures improving self-rescue. The model provides a solution between evacuation modelling, which might be too time-consuming and state-of-the-art QRA-calculations, which have insufficient detail to show the effect of safety measures.

Other factors that are considered in the model are the distance to a safe location and the presence of a bot-tleneck in the evacuation route. The model can be used for the following purposes:

− For fast calculations of the exposure time and the number of persons incapable of self-rescue;

− To determine the effect of safety measures im-proving self-rescue, by calculating the remaining consequences for a scenario after taking meas-ures. Subsequently these consequences can be compared to those of the original scenario in the QRA.

The following sections show the relations for de-scription of the toxic effects and their influence on the mobility or walking velocity. Note that in case of fire, for instance, there can be interaction between toxic exposure and heat exposure: if the mobility de-creases due to toxic exposure (smoke), the exposure time to heat can increase.

3 TOXIC INJURIES

For toxic injuries a distinction is made between as-phyxiant and irritant gases. For an asas-phyxiant prod-uct, such as carbon monoxide, the most important criterion for its toxic effects is the concentration in the blood supply to the brains. On the other hand, for an irritant product the most important factor is the concentration in the lining of the nose, throat, or lung (Purser 2002).

3.1 *Asphyxiant fire products *

The Fractional Incapacitation Dose (FID) model of Purser (Purser 2002) has been selected to describe the effects of asphyxiant fire products for their pres-ence in fire smoke as well as for the pure substance. The FID model relates the toxic dose inhaled by a person to the dose where incapacitation (i.e. loss of consciousness) occurs. The FIN is the sum of the FID values for all asphyxiant fire products, which also accounts for hyperventilation resulting from ex-posure to carbon dioxide. Incapacitation occurs by a (cumulated) exposure to carbon monoxide, hydro-cyanic acid and oxygen deficiency (FINtotal =1) or by

exposure to high concentrations of carbon dioxide (FIDCO2 =1).

## (

(*CO*

*HCN*)* 2

*O*

_{2}

## )

*total* *FID* *FID* *VCO* *FID*

*FIN* = + + (1)

where FIDCO, FIDHCN and FIDO2 = Fractional

Inca-pacitation Dose for CO, HCN and O2 respectively;

CO = carbon monoxide; HCN = hydrocyanic acid; O2=oxygen; CO2 = carbon dioxide; VCO2 =

multi-plication factor hyperventilation [-].

The Fractional Incapacitation Dose is described for CO, HCN, O2, and CO2 by equation 2 to 6 (Purser

2002).
*PID*
*t*
*RMV*
*CO*
*FID _{CO}* =3.317×10−5[ ]1.036 (2)

where [CO] = CO concentration in ppm; RMV =Respiratory Minute Volume in litre/min, which is 25 litre/min at light activity; t = exposure time in min; PID = Personal Incapacitation Dose =30%. The FIDs for oxygen and hydrocyanic acid are de-scribed by equations 3 and 4. Equation 3 and 4 are valid for relatively short exposure time (shorter than 1 hour) and a constant concentration.

)
%
9
.
20
(
*
54
.
0
13
.
8 2
2 *V* *O*
*O*
*e*
*t*
*FID* = _{−} _{−} (3)

where V%O2 = O2 volume percentage;

]
[
*
023
.
0
396
.
5 *HCN*
*HCN*
*e*
*t*
*FID* = _{−} (4)
where [HCN] = HCN concentration in ppm.

Carbon dioxide (CO2) increases the Respiratory

Minute Volume, resulting in a larger uptake rate of other gases. The increase of Respiratory Minute Volume by hyperventilation is described by a multi-plication factor VCO2:

1
.
7
004
.
2
2
%
*
1903
.
0
2
+
=
*CO*
*V*
*e*
*VCO* (5)

where V%CO2 = CO2 volume percentage.

Besides its effect on the Respiratory Minute Vol-ume, CO2 in itself can lead to incapacitation when

present in higher concentrations.

2
2 6.1623 0.5189**V*%*CO*
*CO*
*e*
*t*
*FID* = _{−} (6)

Using equations 1 to 6, the FIN can be determined for toxic fire products within fire smoke as well as for the separate toxic substances.

For asphyxiant fire products the time to incapaci-tation and its severity usually show a short period of intoxication that is followed by a relatively sharp decline into incapacitation (Purser 2002). The rela-tion between FIN and mobility is shown in figure 2 (University of Greenwich, 2004).

0,0 0,2 0,4 0,6 0,8 1,0 0 0,2 0,4 0,6 0,8 1 FIN or FIC M o b il it y f ac to r FIN FIC

Figure 2. Mobility as a function of FIN and FIC

3.2 *Irritant fire products *

Dose calculations are applied for incapacitation ef-fects of asphyxiant fire products as well as for the le-thal effects of irritant fire products. However, the in-capacitation effect of irritant fire products is related to the concentration instead of the dose. The toxic effects are described by the Fractional Irritant Con-centration (FIC) model.

2
2
]
[
]
[
]
[
]
[
]
[ _{2} _{2}
*NO*
*SO*
*HF*
*HBr*
*HCl* *F*
*NO*
*F*
*SO*
*F*
*HF*
*F*
*HBr*
*F*
*HCl*
*FIC*= + + + + (7)

where [HCl] = Hydrochloric acid concentration in ppm; FHCl = threshold concentration for HCl in ppm;

The threshold values for irritant fire products are given in table 1. Incapacitation occurs when the FIC equals unity, for which the toxic effect of different irritant fire products can be added. The relation be-tween FIC and mobility is shown in figure 2 (Uni-versity of Greenwich, 2004).

Table 1. Threshold values for irritant fire products _____________________________________ Toxic gas Severely irritant concentration

(ppm)
_____________________________________
HBr 200
HCl 200
HF 120
NO2 80
SO2 30
_____________________________________
3.3 *Toxic chemicals *
In order to be able to translate the presence of toxic
chemicals into mobility, the methods of FID and FIC
are also applied for releases of toxic chemicals. The
general equations for the FID and FIC methods are:

## ∑

## ∑∑

= = = = ∆ =*n*

*i*

*i*

*i*

*n*

*i*

*t*

*t*

*i*

*i*

*Ct*

*t*

*D*

*t*

*Ct*

*C*

*FID*1 1 0 ( ) ) ( ) ( (8)

## ∑

= =*n*

*i*

*i*

*i*

*F*

*C*

*FIC*1 (9) where Ci = average concentration in ppm of chemi-cal “i” over the chosen time increment; ∆t = chosen time increment in min; Di(t) = dose of chemical i at time t; (Ct)i = the threshold dose in ppm*min; Fi = threshold concentration for chemical “i” in ppm. Because the FID and FIC threshold values are only known for fire products, other threshold values are required for the toxic chemicals. The Acute Expo-sure Guideline Level 2 (AEGL-2) is very suitable for the definition of ability of self-rescue. AEGL-2 is the airborne concentration of a substance above which it is predicted that the general population, in-cluding susceptible individuals, could experience ir-reversible or other serious, long-lasting adverse health effects or

*an impaired ability to escape*. AEGL-2 values are available for exposure durations of 10 minutes, 30 minutes and 1 hour, 4 hours and 8 hours. The subdivision of several chemicals in as-phyxiant and irritant as well as their threshold values are shown in table 2. The chemicals in table 2 are representative for various hazard categories as used in QRAs. The AEGL-2 is not (yet) determined for acrylonitrile and ethylchloride, the Immediately Dangerous to Life and Health (IDLH) value is used for these chemicals. IDLH is defined as a concentra-tion that an exposure up to 30 minutes does not cause death, serious or irreversible health effects, or

*does not impair or impede the ability to escape*. Table 2. Subdivision and AEGL-2 threshold values of toxic chemicals. ________________________________________________ Chemical Subdivision Concentration (ppm) __________________ 10 min 30 min exposure exposure ________________________________________________ Acrylonitrile FID - 85*

Ethyl chloride FID - 3800*

Ammonia FIC 220 220

Chlorine FIC 2.8 2.8 Methylisocyanate FID 0.40 0.13 Nitric acid FIC 43 30 _____________________________________________ * IDLH threshold value

The FID can now be determined by calculating the threshold dose (Ct) from table 2 and inserting this value into equation 8. For instance, the threshold

dose (Ct) for acrylonitrile is 255 ppm*min. The FIC can be determined by taking the threshold concentra-tion from table 2, for nitric acid the value depends slightly on the timescale of the calculations (10 min or 30 min value).

The FID and FIC are translated into a walking ve-locity using the relations shown in figure 2.

4 THERMAL INJURIES

Exposure to thermal radiation is assumed to have
lit-tle or no effect on the mobility of the victims, until
the injuries become lethal. During the self-rescue
pe-riod, the heat radiation to which the person is
ex-posed will decrease with the distance. This is
ac-counted for by calculating the effective exposure
duration (CPR 16E 1992):
×
+
−
×
+
≈
−
3
5
0
0 _{1} _{1}
5
3
*v*
*r*
*eff* *t*
*x*
*u*
*u*
*x*
*t*
*t* (10)

where teff = effective exposure time (s); x0 = the

ini-tial distance to the fire source (m); u = the evacua-tion velocity (m/s); tr = reaction time (= 5 s); tv = (xs

-x0)/u = evacuation time (s); xs = distance from fire

source where heat radiation is below 1 kW/m2 (m). The evacuation velocity, u, can be influenced by exposure to toxic fire products: if the mobility de-creases the exposure time to heat is increased: u = mobility factor * u0, where u0 = maximum

evacuation velocity. The effective exposure time ob-tained with equation 10 can subsequently be used to calculate degree of injuries and lethal victims due to heat exposure.

5 EVACUATION

Two important characteristics of the evacuation route are included in the model, namely the distance to a safe location and the presence of bottlenecks on the evacuation route.

5.1 *Distance to safe location *

The distance to a safe location can be defined by a threshold value (concentration, maximum dose or heat radiation level) or it can be the distance to a place to shelter, such as a building, where windows and doors can be closed. The mobility of a person is influenced by the concentration or toxic dose to which he is exposed on his way to the safe location. In case of fire, the distance to a heat resistant shelter or the distance to 1 kW/m2 (xs) is inserted in

equa-tion 10.

5.2 *Bottlenecks on the evacuation route *

The evacuation calculations within the model are not intended to model the evacuation route in detail. However in cases of important bottlenecks in the route, such as a door or stairs, it can be very impor-tant to be able to model the effect of the bottleneck. The evacuating persons need to pass the bottleneck before reaching a safe location. The actual exposure time increases due to the time necessary to pass the bottleneck. An average value for the extra exposure time due to the bottleneck is given by:

tbottleneck = n/ Cbottleneck (11)

where n = number of persons that need to pass through the bottleneck (-); Cbottleneck = bottleneck

ca-pacity in number of persons per minute.

6 IMPLEMENTATION AND APPLICATION

6.1 *Model implementation *

The model can be implemented in several ways, this chapter describes the following examples:

1 Straightforward implementation for QRA method;

2 Dynamic implementation for scenario analysis or more extensive QRA calculations.

The difference in implementation is the level of de-tail of modelling the effect of toxic exposure to the evacuation velocity.

6.2 *Straightforward implementation method *

For the QRA method a straightforward implementa-tion is often sufficient. In this case the evacuaimplementa-tion velocity is based on the concentration profile on the starting location of the person. For asphyxiant chemicals, the first step is to estimate the exposure time with the maximum evacuation velocity, u=u0, according to:

texp = tr + tbottleneck +(xs-x0)/u; (12)

Subsequently the dose is determined using the con-centration profiles Ci(x0, t) on the starting location of

the person:

## ∫

=*t*

*i*

*i*

*t*

*C*

*x*

*t*

*dt*

*D*0 0, ) ( ) ( (13)

FID and corresponding mobility factor are calcu-lated with the equations in sections 3.1 or 3.3 and figure 2. Subsequently the effective exposure time is determined with equation 12, this time with u= mo-bility factor*u0:

teff = tr + tbottleneck + (xs-x0) / (mobility factor*u0)

In the final step the effective FID is determined us-ing the effective exposure time. The effective FID is used to determine whether a person with a certain starting location will become incapable of self-rescue during his attempt to escape (using figure 2). For irritant chemicals the FIC at the starting posi-tion is determined with the equaposi-tions in secposi-tions 3.2 or 3.3 and the mobility factor is read from figure 2. The effective exposure time can then be calculated with equation 12, assuming u= mobility factor*u0.

The effective exposure time is important input for calculating lethal damage.

6.3 *Dynamic implementation method *

For a scenario analysis the evacuation velocity will be calculated dynamically: when a person moves to another (safer) location, he will be exposed to a lower concentration. Therefore the toxic dose will increase less compared to staying on the same loca-tion. For each time increment ∆t, the FID or FIC and mobility factor are calculated and used as input for the next time increment until a person either reached a safe location or is incapable of self-rescue. For irri-tant chemicals Ci(x,t) is input for equation 9. For

as-phyxiant chemicals the dose is calculated with:

## ∫

=*t*

*i*

*i*

*t*

*C*

*x*

*t*

*dt*

*D*0 ) , ( ) ( (13)

For both irritant and asphyxiant chemicals: x = x0 for t ≤ tr

x = x0 + u(t-tr) for t > tr

u= mobility factor*u0 is determined for each time

increment with FID (as a function of Di(t)) or with

FIC and corresponding mobility factors.

6.4 *Model applications *

When applying the model, a more realistic expo-sure time and therewith a more realistic estimation of the (lethal) damage of this exposure can be calcu-lated. Even more important, is the use of the model to estimate the number of persons in the hazardous area, who are not capable of self-rescue. The FID and FIC can be determined for every exposed person depending on his starting location. If the FID or FIC of a person exceeds unity, that person will be inca-pable of self-rescue. Combining this information on self-rescue with population data yields the total number of persons incapable of self-rescue.

The number of persons incapable of self-rescue is important information for preparation and real-time activities of rescue services. In order to determine

the rescue capacity necessary to handle the accident, the number of persons incapable of self-rescue is more relevant than the number of fatal injuries.

The effects of safety measures improving self-rescue can be determined with the use of the model. An example of a safety measure is increasing the ca-pacity of a bottleneck in the evacuation route or placing a shelter or safe haven.

7 CONCLUSIONS

With state-of the art QRA methods, safety measures for self-rescue cannot yet be assessed. The model described in this paper enables to include self-rescue in QRA methods. The model distinguishes heat ra-diation, smoke and several types of toxic chemicals and quantifies their effect on the walking velocity and exposure duration. Evacuation route characteris-tics considered in the model are the distance to a safe location and the presence of a bottleneck in the evacuation route. The model can be used to deter-mine the number of persons incapable of self-rescue, which is important information for the rescue ser-vices. Furthermore the more realistic exposure times obtained with the model can be used for improving the estimation of lethal damage.

The model can be integrated within a quantitative risk analysis method to directly show the effect of self-rescue improving measures. The model is espe-cially suitable for QRAs involving risks to densely populated locations, such as railway stations, stadi-ums, offices as well as industrial plants and their in-habited surroundings.

NOMENCLATURE

[CO] Carbon monoxide concentration (ppm) AEGL-2 Acute Exposure Guideline Level 2: airborne

concentration of a substance above which it is predicted that the general population, in-cluding susceptible individuals, could ex-perience irreversible or other serious, long-lasting adverse health effects or an impaired ability to escape

Cbottleneck Bottleneck capacity (persons / min)

Ci(x,t) Concentration profile of chemical i (ppm)

FHCl Threshold concentration for HCl (ppm)

FIC Fractional Irritant Concentration (-) FID Fractional Incapacitation Dose (-)

FIN Sum of the FID values for asphyxiant fire products (-)

IDLH Immediately Dangerous to Life and Health (IDLH) value: concentration that an expo-sure up to 30 minutes does not cause death, serious or irreversible health effects, or does not impair or impede the ability to escape

n Number of persons that need to pass through the bottleneck (-)

PID Personal Incapacitation Dose (%) QRA Quantitative Risk Analysis

RMV Respiratory Minute Volume (litre/min) t Exposure time (min)

teff Effective exposure time (s)

tr Reaction time (= 5 s)

tv Evacuation time (s)

u Evacuation velocity (m/s)

u0 Maximum evacuation velocity (m/s)

V%O2 Oxygen volume percentage (%)

VCO2 Multiplication factor hyperventilation (-)

x0 Initial distance to the fire source (m)

xs Distance from fire source where heat

radia-tion is below 1 kW/m2 (m)

REFERENCES

CPR 16E. 1992. Methods for the determination of possible damage to people and objects resulting from releases of hazardous materials. First edition. Committee for the Pre-vention of Disasters caused by dangerous substances. The Hague: directorate-General of Labour of the Ministry of Social Affairs and Employment. ISBN 90-5307-052-4. Purser, P.A. 2002. Toxicity assessment of combustion

prod-ucts, In: *The SFPE handbook of fire protection engineering.*

3rd edition. Quincy, Massachusetts: NFPA. ISBN 087765-451-4.

Uijt de Haag, P.A.M. 2006. “Handleiding Risicoberekeningen BEVI” (Guidelines for quantitative risk analysis, in Dutch). University of Greenwich. 2004. “Building Exodus Manual”.