. . Principles of Smoke
CO and is apparent the formulations of the N- gas and models that follow.
N-Gas Model
The N-gas model was developed at the National Institute of Standards and Technology and relates fatality with animal test data of exposures to pure gases and mixtures of gases (Levin 1996; Levin et al.
1995; Babrauskas et al. 1991). For mixtures of gases, including the N-gas model can be stated as
and for mixtures not including the N-gas model can be stared as
+ -
b 20.9 -
(3.25)
[ H C N ] + +
where
= N-Gas model indicator
= -18 for 5% and 23 for 5%;
= 122,000 for 5% and -38,600 for CO, 5%;
= lethal concentration of
lethal concentration of HCN, ppm;
= lethal concentration of ppm;
= lethal concentration of ppm;
= lethal concentration of ppm;
= time-integrated average exposure to CO,
= time-integrated average exposure to
= time-integrated average exposure to
= time-integrated average exposure to HCN,
= average exposure to
= time-integrated average exposure to
= exposure to H
The model incorporates the breathing rate due to exposure. It is apparent that there is a unique interaction between HCN and For many of the gases, the contribution to lethality is expressed as the ratio of the gas exposure to the This is how is treated, except that it is in terms of oxygen depletion.
The toxicity of is not included in the N-gas model because fire-generated atmospheres do not con- tain toxic concentrations of CO,. The of is 47% and the maximum concentration of in a fire atmosphere is 20.9% if all of the oxygen in the air is converted to
For animal tests, it was found that when the value was approximately I, some of the animals died.
For values below 0.8, there would be no fatalities, and for values above 1.3, all of the animals would be expected to die.
The time-integrated average exposure to CO is
=
[ C O ]
where is the exposure time. The other time-integrated averages can be expressed in a similar manner. For discrete data, the time-integrated average can be writ- ten as follows:
[ C O ] -
e l
- I C,,,.,
l
3 -Smoke and Tenability
= of CO,
= concentration of ppm;
concentration of
concentration of HCN, ppm;
concentration of
= concentration of ppm;
concentration of ppm;
= exposure time, min;
A t time interval
Equation (3.27) can be used where the inter- vals are either uniform or For
intervals, the time-integrated average these equations become mean averages. When the concentra- tion of any of the gases other than is zero, the contri- bution of that gas to the value is also zero. This is to be expected, but it is not so for the fractional incapac- itating dose method discussed later.
Equations (3.24) and (3.25) apply when the expo- sure time is the same as the duration of the data.
Example 3.6 demonstrates the use of the N-Gas model for four gases, but Table 3.9 has values for all of the gases in this model for many exposure times. For
n = number of concentration values for each gas exposure times between those listed in this table,
and time interval. values can be interpolated.
Example 3.6 Using the N-Gas Model . . . for a 20-minute exposure to the mixture of gases listed below.
Time
I (m in) .
0 0 20.90 0 0 0
I 2 20.72 40 2
2 4 20.30 1900 60 3
3 6 19.80 3200 120 6
4 8 19.70 3600 120 6
19.60 3800 I60 8
6 19.60 3 800 500 25
7 19.60 3800 600 30
S I6 19.60 3800 600 30
9 I S 19.60 3800 600 30
20 19.60 600
time-integrated can be calculated from Equation Bccausc the intervals are the integrated average are mean averages of the concentrations as listed
19.8 [CO] 340
[CO,] 3208 [HCN
Bccausc is no exposure to HCI and Equation becomes
Bccausc is 5% (50.000 = -1 8 and =
For a 70-minute exposure. lethal concentrations from Table 3.9 are = 5.2% and = 170 pprn.
This exposure not be expected to cause
Smoke Management
Table 3.9:
Lethal Concentration, of Various Gases
Exposure and they are expected to have similar toxicological effects,
and o f the for were extrapolated
from o f HCI.
Fractional Incapacitating Dose
Purser (2002) developed a to calculate a fractional incapacitating dose for exposures to CO, HCN, and reduced The notation in this section has been modified from that of Purser to facilitate com- puter programming.
whichever is greater, where
fractional incapacitating dose of narcotic gases (dinlensionless);
fraction of an incapacitating dose of CO per unit
= fraction incapacitating dose of HCN per unit time
factor for CO1-induced hyperventilation;
= of an incapacitating dose of oxygen per unit time
= of an incapacitating dose of per unit time
exposure time interval i (min);
n = number of concentration values for each gas and time intervals.
The following are calculated as
where
= concentration of CO (ppm);
= concentration of HCN (ppm);
= concentration of (percent);
= concentration of (percent).
A value of of I or more indicates incapacita- tion. and incapacitation time based on can be taken as the it takes for to become I.
Equation (3.29) represents incapacitation due to the effects of and this equation included for completeness. As previously stated, fire-generated atmospheres do not contain toxic concentrations of Equation (3.29) may be useful for fire scenarios that include sources of other than the fire. For applica- tions where there are no sources of Equa- tion (3.28) should be used for the calculation of
As previously stated, the method is based on air composed of Any combustion calculations or measurements that are used for input to calculations of should be consistent with this concentration.
Examination of Equation (3.30) that for zero CO, has a value of zero;
Chapter 3-Smoke and Tenability
However, items 2 and 3 were unexpected. A z e r o . about 3.3 hours can be calculated for exposure to an concentration of HCN results in a positive contribution atmosphere of and zero concentrations of
to the and oxygen CO, and HCN. This exposure can be thought
results in a positive contribution. For the short exposure times characteristic of most fire protection applications,
in incapacitation. This indicated that the approach is these positive contributions are small and should not be
of concern. inappropriate for long exposures. However, the FED
and the N-gas model are based predominantly on test
the case for the World Trade explosion. From applying these
Equation and an incapacitation time of models for long exposure times is also questionable.
Example Using the Model For the gases of Example 3.6, calculate the
Use Equations (3.28) and (3.30) to calculate the table below. Remember for has units of percent.
Time (min) FIN
0 0 NIA NIA 0
2 0.00 0.00475 1.053 0.000325 0.013
2 4 0.00 19 0.00486 0.000407 0.029
3 6 0.0039 0.0052 1.107 0.000534 0.050
4 0.0033 0.0052 1.115 0.000563 0.072
5 10 0.0053 0.00545 1.119 0.000594 0.097
6 0.0 73 0.00806 1.119 0.000594 0.155
7 0.0209 0.00904 1.119 0.000594 0.223
S 0.0209 0.00904 1.119 0.000594 0.291
9 0.0209 0.00904 1.119 0.000594 0.359
20 0.0209 0.00904 0.000594 0.427
At 20 minutes of exposure, the is about 0.43. This indicates that this exposure is not expected to cause incapacitation.
Example 3.8 Comparison of For the gas concentrations listed below, calculate and
Time
%
0 0 20.90 0 0 0
2 20.18 2320 320 8
2 4 18.50 7600 480
3 6 16.50 12800 960 24
4 8 16.10 14400 960 24
5 15.70 15200 1280 32
6 15200 4000
7 15200 4800
S . 15200
I S 1 4800,
20 15200 4800 120
Part I: In as Example 3.6, is calculated. expected
Principles of Smoke Management
Example 3.8 (Continued) Comparison of Toxicity Models
Part 11: Calculations of FIN are similar to those of Example