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ASTM Selected Technical Papers
Mathematical Modeling of Fires
By
JR Mehaffey
JR Mehaffey
1
National Research Council of Canada
,
Ottawa, Ontario,
Canada
K1A OR6
;
symposium chairman and editor
Search for other works by this author on:
ISBN-10:
0-8031-0992-X
ISBN:
978-0-8031-0992-6
No. of Pages:
143
Publisher:
ASTM International
Publication date:
1988

It is now well established that hydrogen chloride is unusual among common fire gases in that it decays from the atmosphere. No model of hydrogen chloride transport and decay exists as yet, which has been formulated in such a way that it is generic enough to be used for scenarios different from the one in which the experiments were carried out, and can be incorporated into more comprehensive fire hazard models. The present paper introduces such a model. It deals with the influence of various surfaces [poly(methyl methacrylate) (PMMA), painted gypsum board, ceiling tile, cement block and Marinite], of surface to volume ratio and of humidity, on atmospheric hydrogen chloride concentration, both inside and outside the room of origin of the fire.

The present model incorporates generation of hydrogen chloride from poly(vinyl chloride), mass transfer to various wall locations, partition between the atmosphere and the surface, and a combination of diffusion and reaction inside the surface. The parameters in the model were fitted by using a non-linear (Marquardt) optimization procedure.

The model was corroborated using various experiments which involved the combustion of poly(vinyl chloride) in large- and small-scale scenarios.

It was found that, for a non-sorptive surface such as PMMA, the rate of mass transfer to the surface is much larger than the rates of the various reactions at the surface, in all cases. Such a surface, thus, allows much higher peak hydrogen chloride concentrations and much lower rates of decay than any of the sorptive surfaces investigated.

For sorptive surfaces and static systems the rate limiting process is the mass transfer to the surface. The activity of the various surfaces investigated was found to follow the order: ceiling tile > cement > Marinite ≥ painted gypsum board ≫ PMMA

The significance of this model is that it can predict hydrogen chloride decay in a real fire scenario. It is relevant to point out that normal construction surfaces are sorptive, and that hydrogen chloride decay will generally be quite fast in a fire, whereas it will be much slower in a small-scale toxicity test exposure chamber.

1.
Fowell
,
A. J.
,
Fire Technology
 0015-2684, Vol.
21
, p. 199,
1985
.
2.
Jones
,
W. W.
, “
A Model for the Transport of Fire, Smoke, and Toxic Gases (FAST)
,” NBSIR 84-2934,
National Bureau of Standards
, September, 1984.
3.
Mitler
,
H. E.
, and
Emmons
,
H. W.
, “
Documentation for CFC V, the Fifth Harvard Computer Fire Code
,” Harvard University Report to National Bureau of Standards, NBS-GCR-81-344,
1981
.
4.
Smith
,
E. E.
, and
Satija
,
S.
,
Journal of Heat Transfer
 0022-1481, Vol.
105
, p. 281,
1983
.
5.
Cullis
,
C. F.
, and
Hirschler
,
M. M.
,
The Combustion of Organic Polymers
,
Oxford University Press
,
Oxford
,
1981
.
6.
Kaplan
,
H. L.
,
Grand
,
A. F.
, and
Hartzell
,
G. E.
,
Combustion Toxicology
,
Technomic
,
Lancaster, PA
,
1983
.
7.
Chan
,
H. S. O.
,
Journal of Fire Sciences
, Vol.
2
, p. 106,
1984
.
8.
Tsuchiya
,
Y.
, and
Sumi
,
K.
,
Journal of Applied Chemistry
, Vol.
17
, p. 364,
1967
.
9.
Gross
,
D.
,
Loftus
,
J. J.
,
Lee
,
T. G.
, and
Gray
,
E. V.
, “
Smoke and Gases Produced by Burning Aircraft Interior Materials
,”
Building Science Service
, National Bureau of Standards, No.
18
,
1969
, pp. 1-27.
10.
O'Mara
,
M. M.
,
A.C.S. Polymer Preprints
, Vol.
14
, p. 1028,
1974
.
11.
O'Mara
,
M. M.
,
Pure and Applied Chemistry
 0033-4545, Vol.
49
, p. 649,
1977
.
12.
Woolley
,
W. D.
,
Plastics and Polymers
,
1973
, p. 280.
13.
Stone
,
J. P.
,
Hazlett
,
R. N.
,
Johnson
,
J. E.
, and
Carhart
,
H. W.
,
J. Fire Flammability
, Vol.
4
, p. 42,
1973
.
14.
Boudene
,
C.
,
Jouany
,
J. M.
, and
Truhaut
,
J.
,
Macromol. Sci., Chem.
, Vol.
A11
, p. 1529,
1977
.
15.
Edgerley
,
P. G.
, and
Oldland
,
S. R. D.
, in
Proceedings of the Second European Conference on Flammability and Fire Retardants
,
Bhatnagar
V. J.
, Ed.,
Technomic
,
Lancaster, PA
,
1978
, p. 48.
16.
Edgerley
,
P. G.
, and
Pettett
,
K.
,
Plastics and Rubber, Process and Application
, Vol.
1
, p. 133,
1981
.
17.
Martin
,
K. G.
, and
Powell
,
D. A.
,
Fire and Materials
 0308-0501, Vol.
3
, p. 132,
1979
.
18.
Packham
,
S. B.
, and
Crawford
,
M. B.
,
Journal of Fire Sciences
, Vol.
2
, p. 37,
1984
.
19.
Beitel
,
J. J.
,
Bertelo
,
C. A.
,
Carroll
,
W. F.
,
Gardner
,
R. O.
,
Grand
,
A. F.
,
Hirschler
,
M. M.
, and
Smith
,
G. F.
,
Journal of Fire Sciences
, Vol.
4
, p. 15,
1986
.
20.
Bertelo
,
C. A.
,
Carroll
,
W. F.
,
Hirschler
,
M. M.
, and
Smith
,
G. F.
,
Proceedings of the Eleventh International Conference on Fire Safety
,
Hilado
C. J.
, Ed.,
Product Safety Corporation
,
San Francisco
,
1986
, p. 192.
21.
Bertelo
,
C. A.
,
Carroll
,
W. F.
,
Hirschler
,
M. M.
, and
Smith
,
G. F.
,
Proceedings of the First International Symposium on Fire Safety Science
,
Grant
C. E.
and
Pagni
P. J.
, Eds.,
Hemisphere
,
Washington
,
1986
, p. 1079.
22.
Hirschler
,
M. M.
, and
Smith
,
G. F.
,
Combustion Institute, Eastern Section
,
Fall Technical Meeting, Dec. 15–17
,
San Juan, Puerto Rico
,
1986
, pp. 40.1.
23.
Beitel
,
J. J.
,
Bertelo
,
C. A.
,
Carroll
,
W. F.
,
Grand
,
A. F.
,
Hirschler
,
M. M.
, and
Smith
,
G. F.
,
Journal of Fire Sciences
, Vol.
5
, p. 105,
1987
.
24.
Beitel
,
J. J.
,
Carroll
,
W. F.
,
Grand
,
A. F.
,
Hirschler
,
M. M.
, and
Smith
,
G. F.
,
Journal of Fire Sciences
, to be submitted.
25.
Levin
,
B. C.
,
Fowell
,
A. J.
,
Birky
,
M. M.
,
Paabo
,
M.
,
Stolte
,
A.
, and
Malek
,
D.
, “
Further Development of a Test Method for the Assessment of the Acute Inhalation Toxicity of Combustion Products
,”
National Bureau of Standards
, NBSIR 82-2532,
1982
.
26.
Crank
,
J.
,
The Mathematics of Diffusion
,
Clarendon Press
,
Oxford
,
1975
.
27.
Welty
,
J. R.
,
Wicks
,
C. E.
, and
Wilson
,
R. E.
,
Fundamentals of Momentum, Heat and Mass Transfer
, second edition,
John Wiley
,
New York
,
1976
.
28.
Carberry
,
J. J.
,
Chemical and Catalytic Reaction Engineering
,
McGraw-Hill
,
New York
,
1976
.
29.
ASPEN PLUS® Electrolytes Manual
,
ASPEN Technology, Inc.
,
Cambridge, MA
,
1984
.
30.
Fenton
,
D. L.
, and
Ranade
,
M. B.
,
Environmental Science and Technology
 0013-936X, Vol.
10
, p. 1160,
1976
.
31.
Hindmarsh
,
A. C.
, “
LSODE and LSODI, Two New Initial Value Ordinary Differential Equation Solvers
,”
ACM-SIGNUM Newsletter
, Vol.
15
, No.
4
,
1980
, p. 10.
32.
Marquardt
,
D. W.
,
Journal of the Society for Industrial Applied Mathematics
, Vol.
11
, No.
2
,
1963
, p. 431.
33.
Jones
,
W. W.
, “
A Review of Compartment Fire Models
,”
National Bureau of Standards
, NBSIR 83-2684,
1983
.
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