No

JD

a

b

1

Fusamdte

rbpmhmtce

Pb

0d

Process Safety and Environmental Protection 8 8 ( 2 0 1 0 ) 109–113

Contents lists available at ScienceDirect

Process Safety and Environmental Protection

journa l homepage: www.e lsev ier .com/ locate /psep

ew Probit equations for the calculation of thermal effectsn humans

uan Francisco Sánchez Péreza, Enrique González Ferradásb, Fernando Díaz Alonsob,∗,aniel Palacios Garcíab, María Victoria Mínguez Canob, José Ángel Bautista Cotorrueloa

Department of Health, Directorate General of Public Health - Service for Environmental Health, Murcia, SpainDepartment of Chemical Engineering, University of Murcia, Campus Universitario de Espinardo, 30100 Murcia, Spain

a b s t r a c t

In this paper new Probit equations are proposed to estimate damage produced by thermal radiation on humans

(for first- and second-degree burns). They are compared to empirical threshold values and also to existing Probit

equations. Results obtained are in good agreement with previous empirical experience. They also provide better

estimations than existing equations. When an analysis is performed to study the evolution in the percentage of

affected people by different degrees of damages, results show that proposed equations produce more consistent

results than existing equations.

© 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Thermal effects; Damage; Probit; First-degree burns; Second-degree burns

. Introduction

lammable substances – mainly oil derivates – are often man-factured, used or transported in chemical industries. Theseubstances can produce different types of fires. Most of themre caused by leaking from storage vessels, different equip-ent or transport containers (Lees, 1996). Subsequent process

evelopment depends on a series of factors (substance proper-ies, velocity of spill or leaking, immediate or retarded ignition,tc).

From the point of view of emergency planning, thermaladiation dose is the most dangerous effect from hydrocar-on fires outdoors. Another important risk from fires is theroduction of toxic substances and smoke, but this is muchore important indoors, where restricted ventilation allows

igh toxic concentrations. On the contrary, this is usually ainor danger outdoors, since vertical thermal transport takes

oxic products away from ground level, unless atmosphericonditions make dispersion very difficult (González Ferradást al., 2002).

In this paper thermal effects from fires are studied and newrobit equations are proposed to estimate damage producedy thermal radiation (for first- and second-degree burns).

∗ Corresponding author.E-mail address: ferdiaz@um.es (F.D. Alonso).Received 31 January 2009; Received in revised form 24 November 2009

957-5820/$ – see front matter © 2009 The Institution of Chemical Engioi:10.1016/j.psep.2009.11.007

2. Effects of fires on human population

The main effect produced by thermal radiation on humansis the generation of burns on the skin, having different levelof gravity depending, among other factors, on the type offire – which will determine temperature and exposure time– on how extensively burned the person is and on the depthof the most serious part of the burn. For example, poolfires will allow the exposed people to run away from theemission point, whereas in flash or jet fires the possibility ofprotection decreases because both are almost instantaneousphenomena.

The area of skin affected by thermal radiation is an impor-tant factor as regards mortality. Rew (1997) assumed thatfatality is primarily dependent on full thickness burn area withprobability of death related to the burn area model of Clarkand Fromm (1987). Bull (1971) shows a relationship betweenfatality, age and percentage of damaged skin area.

In general, thermal radiation effects on humans are twotypes: physiologic and pathologic. First are less important and

; Accepted 25 November 2009

are characterized by increasing heart rhythm, slight increasein body temperature or transpiration. Pathologic effects arecharacterized by burns produced as a consequence of heat

neers. Published by Elsevier B.V. All rights reserved.

al Protection 8 8 ( 2 0 1 0 ) 109–113

Fig. 1 – Experimental data obtained by Buettner (1951b)

110 Process Safety and Environment

absorption through the skin. Burns are usually classified in thefollowing categories: first-, second- and third-degree burns.This classification is based on how extended and deep thedamage is.

First-degree burns produce a superficial damage, causingredness, pain and swelling. First-degree burns cause minimaltissue damage and they only involve the epidermis (skin sur-face). No blisters appear and no medical assistance is required,since damage produced is reversible in the period of 1 or 2days.

Second-degree (partial thickness) burns affect both theouter-layer (epidermis) and the under lying layer of skin (der-mis) causing redness, pain, swelling and blisters. Medicaltreatment is necessary to heal the damaged area (Marx et al.,2002).

Third-degree (full thickness) burns affect the epidermis,dermis and hypodermis, causing charring of skin or a translu-cent white colour, with coagulated vessels visible just belowthe skin surface. Healing from third-degree burns is very slowdue the skin tissue and structures being destroyed. Third-degree burns are vulnerable to infections and require urgentmedical treatment. Damage produced is often irreversible(Marx et al., 2002).

The burn-degree is related to the skin temperature, whichdepends on thermal radiation intensity and exposure time.Some authors – Buettner (1951a), Hardee and Lee (1977) – havecorrelated skin temperature at different depth with exposuretime. But temperature is not the right parameter to establishdamage level. It is more adequate to use “thermal radiationdose”, which shows the relationship between damage and thefollowing parameters: thermal radiation intensity (I, W/m2)and exposure time (te, s). The most accepted expression fordose (D, (W/m2)4/3 s) is indicated in Eq. (1) (TNO, 1989; Shield,1995).

D = I4/3 · te (1)

3. Probit equations for the calculation ofthermal effects in fires

Probit equations (Finney, 1971) allow the correlation of theeffect of thermal radiation to percentage of people affected fora certain level of damage (e.g., first-, second- or third-degreeburns). Probit (Y) is a dimensionless number that correlatesdirectly to the percentage of affected population (see TNO,1989).

TNO (1989) proposed Probit equations to calculate percent-age of people affected by thermal radiation.

For first-degree burns:

Y = −39.83 + 3.0186 Ln (D) (2)

For second-degree burns:

Y = −43.14 + 3.0186 Ln (D) (3)

For third-degree burns:

Y = −36.38 + 2.56 Ln (D) (4)

These equations have been obtained from lethality data

for different magnitudes of nuclear weapons. As wavelengthof thermal radiation produced by hydrocarbon fires is longerthan in nuclear explosions, thermal energy transmitted in

showing the relationship between radiation intensity andexposure time to reach pain sensation.

hydrocarbon fires is thus bigger. For this reason, the origi-nal equations from nuclear explosions (Eisenberg et al., 1975)were modified by TNO using some experimental data (Stolland Chianta, 1969) to obtain Eqs. (2)–(4) (TNO, 1989).

To deal with the problem of insufficient data, TNO (1989)assumed that, for different types of damage with similar con-ditions of exposure, the gradient of the Probit functions areequal. This assumption was used to derive second-degreeburn equation from first-degree burn equation.

In this paper, these equations are analysed based onempirical information and new Probit equations are proposedto determine damage produced by first- and second-degreeburns. These equations may be more consistent and conser-vative than the TNO equations.

3.1. First-degree burns

Using the empirical data obtained by Buettner (1951b), seeFig. 1, the following dose value can be obtained:

D = I4/3 · te ≈ 115 (kW/m2)4/3

s (5)

Taking into account that these data represent the doseneeded to reach pain sensation, it has been assumed that theyrepresent the threshold value to produce first-degree burns.

This threshold value is assumed to correspond to the dosethat would be needed to produce first-degree burns in 1% ofthe exposed population. This corresponds to a Probit value of2.67.

Fitting the empirical data from Buettner (1951b) and theabove-mentioned Probit value to the general form of a Probitequation and using the gradient proposed by TNO equation,the following expression is obtained:

Y = −11.65 + 6.95 log (D) (6)

where D ((kW/m2)4/3 s) is also calculated using Eq. (1), but I in

(kW/m2).

Bagster and Pitblado (1989) showed that a dose of118 (kW/m2)4/3 s – 4.7 kW/m2 during 15 s – was the thresh-

Protection 8 8 ( 2 0 1 0 ) 109–113 111

o(aaal(

dt

aB1

3

Uao

D

nto

too

mae

Y

oLa

Process Safety and Environmental

ld value for burns. The same radiation intensity value4.7 kW/m2) had already been proposed by Robertson (1976)s limit for pain but without blisters – first-degree burns –lthough no exposure limit was indicated. Considering thatthreshold value is affecting approximately 1% of the popu-

ation, a comparison can be performed between Eqs. (2) and6).

Calculating the Probit for 4.7 (kW/m2) during 15 s, twoifferent results are obtained for Eq. (2) and for Eq. (6), respec-ively.

For Eq. (2), Y = 2.67, D = 130 (kW/m2)4/3 s.For Eq. (6) as mentioned above, Y = 2.67, D = 115 (kW/m2)4/3 s.

As it can be observed, both results in the same range,lthough dose value obtained with Eq. (6) – from data byuettner (1951a,b) – is closer to the empirical value of18 (kW/m2)4/3 s obtained by Bagster and Pitblado (1989).

.2. Second-degree burns

sing the empirical data obtained by Stoll and Greene (1952)nd Metha et al. (1973), Fig. 2, the following dose value can bebtained:

= I4/3 · te ≈ 250 (kW/m2)4/3

s (7)

Taking into account that these data represent the doseeeded to start second-degree burns, it has been assumedhat they represent the threshold value to produce this typef burns.

This threshold value is assumed to correspond to the dosehat would be needed to produce second-degree burns in 1%f the exposed population. This corresponds to a Probit valuef 2.67.

Fitting the empirical data corresponding to the above-entioned dose and the Probit value to the general form ofProbit equation and using the gradient proposed by TNO

quation, the following expression is obtained:

= −13.87 + 6.95 log (D) (8)

For second-degree burns, Bagster and Pitblado (1989)

btained a dose threshold value of 236 (kW/m2)4/3 s, whereasihou and Maund (1982), fitting experimental data from Stollnd Chianta (1971), obtained a value of 239 (kW/m2)4/3 s.

Table 1 – Percentage of population affected by first-degree burn900 (kW/m2)4/3 s. Results obtained from Eqs. (2) and (6).

Eq. (6)

Dose (kW/m2)4/3 s Probit (Y) Percentage of affectedpopulation (%)

900 8.88 100800 8.53 100700 8.12 100600 7.66 99.6500 7.11 98400 6.43 92300 5.57 72250 5.02 51200 4.34 25115 2.67 1100 2.25 0

Fig. 2 – Experimental data from Stoll and Greene (1952) andMetha et al. (1973) for second-degree burns.

Considering that a threshold value is affecting approxi-mately 1% of the population, the same comparison carried outfor first-degree burns can now be performed for second-degreeburns between Eqs. (3) and (8).

For Eq. (3), Y = 2.67, D = 390 (kW/m2)4/3 s.For Eq. (8) as indicated above, Y = 2.67, D ≈ 250 (kW/m2)4/3 s.

In this case, Eq. (8) is much closer to the empirical observa-tions than Eq. (3).

In fact, if we use Eq. (3) to calculate the percentage of pop-ulation affected by a dose of 236–239 (kW/m2)4/3 s, the resultobtained is close to 0% and falls out of the table provided byTNO to calculate the percentage from the Probit, which is notconsistent with the definition of threshold value.

3.3. Third-degree burns

No empirical data have been found for third-degree burns to

assess Eq. (4), so no alternative equation is proposed in thispaper. For the analysis below, Eq. (4) is always used to calculatethird-degree burns.

s for different dose values between 100 and

Eq. (2)

Dose (kW/m2)4/3 s Probit (Y) Percentage of affectedpopulation (%)

900 8.51 100800 8.15 100700 7.75 99.7600 7.28 99500 6.73 96400 6.06 86300 5.19 58250 4.64 36200 3.97 15115 2.30 0100 1.87 0

112 Process Safety and Environmental Protection 8 8 ( 2 0 1 0 ) 109–113

Table 2 – Percentage of population affected by second-degree burns for different dose values between 100 and900 (kW/m2)4/3 s. Results obtained from Eqs. (3) and (8).

Eq. (8) Eq. (3)

Dose(kW/m2)4/3 s

Probit (Y) Percentage of affectedpopulation (%)

Dose(kW/m2)4/3 s

Probit (Y) Percentage of affectedpopulation (%)

900 6.66 95 900 5.20 58800 6.31 90 800 4.84 44700 5.90 82 700 4.44 29600 5.44 67 600 3.97 15500 4.89 46 500 3.42 6400 4.21 22 400 2.75 1300 3.35 5 300 1.88 0250 2.80 1 250 1.33 0200 2.12 0 200 0.66 0115 0.45 0 115 −1.01 0100 0.03 0

Table 3 – Percentage of population affected bythird-degree burns for different dose values between 100and 900 (kW/m2)4/3 s. Results obtained from Eq. (4).

Dose (kW/m2)4/3 s Probit (Y) Percentage of affectedpopulation (%)

900 4.61 35800 4.31 24700 3.97 15600 3.57 8500 3.11 3400 2.54 1300 1.80 0250 1.33 0200 0.76 0115 −0.65 0

100 −1.01 0

4. Analysis of the coherence in thecumulative results for different burn-degrees

An analysis of the results obtained from the above-mentionedequations for different dose values is performed in order toassess the coherence of the results.

For each burn-degree, percentage of affected population iscalculated for dose between 100 and 900 (kW/m2)4/3 s. Resultsare shown in Tables 1–3.

As it can be observed for some thermal dose values, theaddition of affected population from first-, second- and third-degree burns is higher than 100%. This must be interpreted

Table 4 – Percentage of population affected by first-, second- an100 and 900 (kW/m2)4/3 s. Results obtained from Eqs. (2)–(4), (6)

Eq. (4), (6) and (8)

Dose(kW/m2)4/3 s

First-degree(Eq. (6))

Second-degree(Eq. (8))

Third-degree(Eq. (4)) (k

900 5 60 35800 10 66 24700 18 67 15600 32.6 59 8500 52 43 3400 70 21 1300 67 5 0250 50 1 0200 25 0 0115 1 0 0100 0 0 0

100 −1.44 0

considering that upper damage levels are included in the lowerones. Obviously, people affected by third-degree burns are alsoaffected by second- and first-degree burns.

Thus, actual percentage of people whose most seriousinjury is second-degree burns must be obtained by discount-ing the percentage of people suffering third-degree burns (Eq.(4)) from the total amount of people suffering second-degreeburns (Eq. (3) or (8)). In the same way, actual percentage ofpeople affected only by first-degree burns must be obtained bydiscounting the actual percentage of people suffering second-degree burns (obtained by means of the above-mentionedcorrection) from the total amount of people suffering first-degree burns (Eq. (2) or (6)). These corrections have beentaken into account to elaborate Table 4, which shows thecorrected results of population affected by different typeof burns when receiving a thermal dose between 100 and900 (kW/m2)4/3 s.

As shown in Table 4, some of the results obtained with Eqs.(3) and (4) are not consistent, as for dose values from 900 to400 (kW/m2)4/3 s, percentage of exposed population affectedby second- and third-degree burns are almost identical.

As indicated above, people affected by third-degree burnsare also affected by second- and first-degree burns, so it’s obvi-ous that percentage of people affected by second-degree burnsmust be higher than people affected by third-degree burns.This is confirmed by Lees (1996), who indicates the results

found in a survey of five American hospitals of 179 people suf-fering from burns; almost 40% had second-degree burns and16% third-degree burns.

d third-degree burns for different dose values betweenand (8), correcting the results as indicated above.

Eqs. (2)–(4)

DoseW/m2)4/3 s

First-degree(Eq. (2))

Second-degree(Eq. (3))

Third-degree(Eq. (4))

900 42 23 35800 56 20 24700 70.7 14 15600 84 7 8500 90 3 3400 85 0 1300 58 0 0250 36 0 0200 0 0 0115 0 0 0100 0 0 0

Prot

5

Idatoa

dpic

R

B

B

B

B

C

E

F

TNO, 1989. Methods for the determination of possible damage.

Process Safety and Environmental

. Conclusions

n this paper new Probit equations are proposed to estimateamage produced by thermal radiation on humans (for first-nd second-degree burns). They are compared to empiricalhreshold values and also to existing Probit equations devel-ped by TNO. Results obtained are consistent and are in goodgreement with previous empirical experience.

The evolution in the percentage of affected people forifferent thermal doses show that equations proposed alsoroduce consistent results in line with previous studies, show-

ng that the proposed equations may be more consistent andonservative than the TNO equations.

eferences

agster, D.F. and Pitblado, R.M., 1989, Thermal hazards in theprocess industry. Chem Eng Prog, 7: 69–75.

uettner, K., 1951, Effects of extreme heat and cold on humanskin. I. Analysis of temperature changes caused by differentkinds of heat application. J Appl Physiol, 3: 691–702.

uettner, K., 1951, Effects of extreme heat and cold on humanskin. II. Surface temperature, pain and heat conductivity inexperiments with radiation heat. J Appl Physiol, 3: 703–713.

ull, J.P., 1971, Revised analysis of mortality due to burns. MedicalResearch Council Industrial Injuries and Burns Unit,Birmingham Accident Hospital, Birmingham. Lancet,1133–1134.

lark W.R., and Fromm, B.S., 1987. Burn Mortality – Experience ata Regional Burn Unit. Acta Chirugica ScandinavicaSupplementum 537, Stockholm.

isenberg, N.A., Lynch, C.J., and Breeding, R.J., 1975. Vulnerabilitymodel: a simulation system for assessing damage resultingfrom marine spills (VMI). US Coast Guard, Office of Researchand Development, Report n◦. CGD-137-75, NTISAD-015-245.

(Cited by TNO, 1989).

inney, D.L., (1971). Probit analysis. (Cambridge University Press,London).

ection 8 8 ( 2 0 1 0 ) 109–113 113

González Ferradás, E., Ruiz Boada, F., Minana Aznar, A., NavarroGómez, J., Ruiz Gimeno, J. and Martínez Alonso, J., (2002).Zonas de planificación para accidentes graves de tipo térmico, (en elámbito del Real Decreto 1254/99 (Seveso II). (Departamento deIngeniería Química Universidad de Murcia, Dirección Generalde Protección Civil, Ministerio del Interior, Madrid).

Hardee, H.C. and Lee, D.O., 1977, A simple conduction model forskin burns resulting from exposure to chemical fireballs. FireRes, 1: 199–205.

Lees, F.P., (1996). Loss Prevention in the Process Industries (2nd ed.).(Butterworth-Heinemann, London).

Lihou, D.A. and Maund, J.K., 1982, Thermal radiation hazard fromfireball, In I Chem E Symposium Series, 71, The Assessment ofMajor Hazards Symposium , pp. 191–224.

Marx, J.A., Hockberger, R.S., & Walls, R.M. (eds) 2002, Rosen’sEmergency Medicine: Concepts and Clinical Practice. (Mosby, St.Louis)

Metha, A.K., Wong, F., and Williams, G.C., 1973. Measurement offlammability and burn potential of fabrics. Summary Reportto NSF-Grant #GI-31881 (Fuels Research Laboratory,Massachusetts Institute of Technology, Cambridge, MA).

Rew, P.J., 1997. LD50 Equivalent for the Effects of ThermalRadiation on Humans. HSE Contract Research Report No.129/1997 (Health and Safety Executive (HSE) Books, Suffolk,UK).

Robertson, R.B., 1976, Spacing in chemical plant design againstloss by fire, In I Chem E Symposium Series, 47, Accidental release,assessment containment and control (p. 157).

Shield, S.R., 1995, The modelling of BLEVE fireball transients, In IChem E Symposium Series, 139 (5th ed., pp. 227–236).

Stoll, A.M. and Greene, L.C., 1952, Relationship between pain andtissue damage due to thermal radiation. J Appl Physiol, 14:373–382.

Stoll, A.M. and Chianta, M.A., 1969, Method and rating system forevaluation of thermal radiation. J Appl Physiol, 14: 373–382(Cited by TNO, 1989)

Stoll, A.M. and Chianta, M.A., 1971, Trans N Y Acad Sci, 649–670.

“The green book” CPR 16E. CIP-data of the Royal Library (TheHague, The Netherlands).