Probit equation

Table 2-5 lists a variety of probit equations for a number of different types of exposures. The causative factor represents the dose V. The probit variable Y is computed from... 

The NIOSH web site states that deaths occur as a result of ammonia exposures between 5,000 and 10,000 ppm over a 30-min period. Compare the result to the results from the probit equation (Table 2-5). 

Use the probit equation (Equation 2-5) to determine the expected fatalities for people exposed for 2 hours to each of the IDLH concentrations of ammonia, chlorine, ethylene oxide, and hydrogen chloride. 

Change the concentration exponent value to 2.00 instead of 2.75 in the probit equation, and rerun your spreadsheet for a total release amount of 5 kg. How sensitive are the results to this exponent ... 

Injury to personnel is determined using probit equations from Table 2-5. The probit equation for deaths resulting from lung hemorrhage is... 

Substituting this value into the probit equations yields... 

Use a spreadsheet program (such as Quattro Pro or Excel) to estimate the total number of fatalities resulting from the burning fireball. Use the probit equations provided in the text. Assume that 400 people are distributed evenly at a distance of 75 m to 1000 m from the fireball center. Divide the distance interval into a number of small increments. Use a small enough distance increment so that the results are essentially independent of the increment size. 

Probit Equation The probit equation has been used in an attempt to quantitatively correlate hazardous material concentration, duration of exposure, and probability of effect/injury, for several types of exposures. The objective of such use is to transform the typical sigmoidal (S-shaped) relationship between cause and effect to a straight-line relationship (Mannan, Lees Loss Prevention in the Process Industries, 3d ed., p. 9/68, 2005). 

Probit equations have the following form (Mannan, Lees Loss Prevention in the Process Industries, 3d ed., Table 9.29, 2005) ... 

The effects of the release of a toxic material are proportional to both its airborne concentration and the duration of the release that is, the greater the concentration or time of exposure, the greater the consequences to those who are exposed. The toxic effect can be expressed mathematically in a probit equation that calculates the probability of damage, Y (CCPS, 1989a). The equation is... 

Values for the constants in the probit equation (3-1) for a few compounds can be found in Guidelines for Chemical Process Quantitative Risk Analysis (CCPS, 1989a, Table 2.9, p. 156). 

The probit equation shows that the percentage of the population affected by an event goes up by a disproportionately small amount as the magnitude of the event increases. For example, if the values shown in Table 14.7 are assigned to the terms in Eq. (14.4) it can be seen that, if the event increases in size by a factor of a 100, the factor affecting the percentage of people impacted by the event goes from 19.5% to 33.4%. 

Using the probit equations of Appendix B the probabilities of death are to be determined which correspond to the ERPG values of Table 2.35. An exposure time of one hour is be used, which is the reference duration for the ERPG values. 

In order to assess the probabilities of death the probit equations (B3c) for ammonia and (B5) for hydrogen cyanide of Appendix B are used. Since both require arguments in ppm, firstly the concentrations are converted according to Eq. (2.54)... 

Health consequences are assessed using the corresponding probit equation (B20) for death due to exposure to hydrogen sulphide. This requires the concentration to be converted into ppm according to Eq. (2.54), which gives... 

The assessment of accident consequences is treated in Chap. 10. It requires numerous phenomena to be modelled such as discharge, atmospheric dispersion or heat radiation of fires. Additionally, relations are needed which relate the intensity of exposure of humans and environment with probabilities for certain volumes of damage. This is often done using probit equations (vid. Sect. 2.6.2.2 and Appendix B). 

Probit equations for determining conditional probabilities of death from... 

The form of Eq. (4) and the shape of the curves in Fig. 16.2 show that there is not a single toxic dose. In other words, the product C x f is not constant. Higher concentrations of chlorine are more dangerous than the assumption of a toxic dose would indicate. This seems to be a widespread if not a general phenomenon. When the independent variable in the probit equation is expressed as C"t, the exponent normally is greater than 1.0. Lees [83] gives an approximate value of 2.75 for both ammonia and chlorine. 

Probit equations for the probit variable, Y, are based on a causative variable, V (representing the dose), and at least two constants. These equations are of the form,... 

Probit equations are available for a variety of exposures, including exposures to toxic materials, heat, pressure, radiation, impact, and sound, to name a few. For toxic exposures, the causative variable is based on the concentration for... 

The output from the spreadsheet solution to this problem is shown in Figure 4.6. The probit equation is fit using a least-squares line fitting technique supported by the spreadsheet. 

Probit equations for a number of different vapor exposures arc provided in Table 4.5. 

TABLE 4.5. Probit Equation Constants for Lethal Toxicity... 

Probit equation parameters for individual gases arc usually derived from animal experiments. Accurate concentrations and duration values are rarely available for historical toxic accidents, but approximate estimates may be derived in some cases to complement the animal data. Probit equation parameters for gas mixtures are not currently available. 

Prugh (1995) also performs a detailed analysis for chlorine, demonstrating that Eq. (4.5), with a fixed exponent w, fits the available data at high concentrations, but not at low. This implies that the probit equation and Eq. (4.5) docs not fit the data over wide concentration ranges. He concludes that this might be true for other chemical species. 

Predictions of gas doud concentrations and durations are available from neutral and dense gas dispersion models (Section 2.3). IDLH and other acute toxic criteria are available for many chemicals and arc described by AIChE/CCPS (1988b). Probit equations are readily applied using spreadsheet analysis, but are not as readily available. 

The spreadsheet output for this example is shown in Figure 4.7. The spreadsheet has been generalized so that the user can specify as input any general probit equation form. 

A fixed mass of toxic gas has been released almost instantaneously from a process unit. The release occurs at night with calm and clear conditions. If the gas obeys the probit equation for fatalities... 

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