Arch. Min. Sci., Vol. 54 (2009), No 3, p. 507–530

Arch. Min. Sci., Vol. 54 (2009), No 3, p. 507–530

Arch. Min. Sci., Vol. 54 (2009), No 3, p. 507–530
507
Electronic version (in color) of this article is available: http://mining.archives.pl
JAN WACHOWICZ*, TOMASZ JANOSZEK*
MATHEMATICAL MODEL OF CONVEYOR BELT FIRE IN MINE GALLERIES
MODEL MATEMATYCZNY POŻARU TAŚM PRZENOŚNIKOWYCH W WYROBISKACH
CHODNIKOWYCH KOPALŃ
The use of organic materials and plastic products, and particularly conveyor belts, in hard coal mines
creates a serious, potential hazard of spontaneous fire occurrence. The article presents the possibility to
use the developed mathematical model when predicting the basic physical parameters determining directly
the phenomenon of conveyor belt fire for the improvement of occupational safety in hard coal mines.
Despite of rigorous enforcement of guidelines comprised in standards concerning fire-resistant belts
and sharpened safety measures, still occurs the fire hazard connected for instance with the self-heating
susceptibility of abrasion products of rubber treats of conveyor belts, fulfilling the compulsory in the
mining sector fire-resistance criteria.
On the ground of results of conveyor belt tests conducted on the basis of the cone calorimeter method
and fire gallery method some mathematical models were formulated, allowing to analyse the open fire
phenomenon in the presence of organic material. The dynamics of conveyor belt fire was expressed by
parameters determining directly the processes occurring during the fire, which are:
• amount of heat released from fire, Qν (formula 1),
• area of the conveyor belt covered by combustion, Αр, and heat exchange
area, Ac for data received from the conical calorimeter and fire gallery (formulas 2 and 5),
• length of burned conveyor belt, LΔt (formula 6),
• temperature of mixture of air and fire gases leaving conveyor belt fire for data obtained from the
fire gallery Ta (formula 9) and Tf (formula 10).
Using the Thorton’s rule, according to which the heat emitted during combustion per
oxygen consumption unit is a constant value (E = 13.1 MJ kg-1), the dynamics of changes of
oxygen concentration in the roadway working (formula 14) and mass share of carbon monoxide
(formula 16) and carbon dioxide in fire gases leaving the fire focus were estimated.
For the correctness assessment of the developed mathematical model the test results
obtained on the basis of the method of conveyor belt flammability tests in the fire gallery and
method of oxygen consumption calorimetry were used, comparing the values of initial variables
from the model with real values, through the determination of the matching quality index. It
has been accepted that the index allowing to assess if the initial variables from the model are
consistent with the general knowledge and experience is the index of correlation r. In the work
the results of tests of chloroprene conveyor belt marked with the symbol 69/97 were used.
*
CENTRAL MINING INSTITUTE, PL. GWARKÓW 1, 40-160 GLIWICE, POLAND
508
On the basis of the determined in the cone calorimeter for radiation intensity 50 kWm-2 and 75kWm-2
value of heat emission rate QHRR as well as calculated value of fire surface Aр and combustion process
efficiency χ, calculations were carried out (formula 9) aiming at the determination of the temperature
value of mixture of air and fire gases Ta. The determined on the basis of the model changes of temperature
and real values measured in the fire gallery were presented in Fig. 4-2. Furthermore, in the Fig. 4-4, 4-5,
and 4-6 the calculated, predicted values of changes of oxygen concentration XO2 in the roadway working
(formula 14) as well as carbon dioxide XCO2 emissions (formula 19) and carbon monoxide XCO emissions
(formula 16) were presented.
Using the simple regression analysis, the existence of correlation between the value of temperatures
determined from the mathematical model for radiation intensity 50kWm-2 and 75kWm-2, towards the real
temperature measured in the fire gallery was pointed out. The best correlation for the values of temperatures
measured from the mathematical model described by the dependences (8) and (9), amounting to r = 0.9,
was obtained basing on the linear model, what proves the existence of a very strong linear dependence
between the tested variables.
Similarly as in the case mentioned above, the simple regression analysis was used in order to point
out the existence of correlation for the values of O2, CO and CO2 molar share calculated from the mathematical model. In the case of oxygen O2 molar share, calculated from the mathematical model (formula 14), the best correlation r = 0.98 was obtained basing on the linear model, what proves the existence of
a very strong linear dependence between the tested variables (Fig. 5-2.1). However, in the case of carbon
monoxide CO molar share, determined from the mathematical model (formula 16), the existence of a very
strong dependence between the tested variables proves the obtained correlation coefficient r = 0.92, and
in the case of carbon dioxide CO2 molar share determined from the mathematical model (formula 19),
the correlation coefficient amounted to r = 0.90.
Summing up it should be stated that on the basis of a detailed analysis of phenomena of conveyor belt
fire a mathematical belt fire model was developed. The existence of considerable correlation between the
results obtained on the basis of the mathematical model and the results obtained by means of experiments
for the real system was pointed out. The determined on the basis of mathematical models values of initial
variables allow a simple and easy interpretation of phenomena occurring during the fire and can be helpful
for the analysis of fire hazards connected with the application of conveyor belts in mines.
Keywords: mathematical model, underground fires, materials flammability, conveyor belt
Stosowanie w kopalniach węgla kamiennego materiałów organicznych i wyrobów z tworzyw sztucznych, a w szczególności taśm przenośnikowych, stwarza poważne, potencjalne zagrożenie zaistnienia
pożaru egzogenicznego. W artykule przedstawiono możliwość wykorzystania opracowanego modelu
matematycznego przy prognozowaniu podstawowych parametrów fizycznych bezpośrednio determinujących zjawisko pożaru taśm przenośnikowych dla poprawy bezpieczeństwa pracy w kopalniach węgla
kamiennego. Pomimo rygorystycznego egzekwowania wytycznych zawartych w normach dotyczących
trudnopalności taśm i zaostrzonych środków bezpieczeństwa ciągle występuje zagrożenie pożarowe
związane np. ze skłonnością do samozagrzewania się produktów ścierania bieżników gumowych taśm
przenośnikowych spełniających obowiązując w górnictwie kryteria trudnopalności.
Na podstawie wyników badań taśm przenośnikowych prowadzonych w oparciu o metodę kalorymetru stożkowego oraz sztolni pożarowej sformułowano pewne modele matematyczne pozwalające
analizować zjawisko pożaru egzogenicznego w obecności materiału organicznego. Dynamikę pożaru
taśmy przenośnikowej wyrażono parametrami bezpośrednio determinującymi zachodzące w czasie
pożaru procesy, którymi są:
• obciążenie cieplne pożaru, Qv (wzór 1),
• pole powierzchni taśmy przenośnikowej objętej spalaniem, Ap, i powierzchni wymiany ciepła,
Ac, dla danych otrzymanych z kalorymetru stożkowego oraz sztolni pożarowej (wzór 2 i 5),
• długość odcinka spalonej taśmy przenośnikowej, LΔt (wzór 6),
• temperatura mieszaniny powietrza i gazów pożarowych opuszczających ognisko pożaru taśmy
przenośnikowej dla danych uzyskanych ze sztolni pożarowej Ta (wzór 9) i Tf (wzór 10).
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Wykorzystując regułę Thortona, według której ciepło wydzielone podczas spalania na jednostek
zużycia tlenu jest wartością stałą (E = 13,1 MJ kg-1), oszacowano dynamikę zmian stężenia tlenu w wyrobisku chodnikowym (wzór 14) oraz udział masowy tlenku węgla (wzór 16) i dwutlenku węgla (wzór 19)
w gazach pożarowych opuszczających ognisko pożaru.
Do oceny poprawności opracowanego modelu matematycznego wykorzystano wyniki badań uzyskane
w oparciu o metodę badania palności taśm przenośnikowych w sztolni pożarowej i metodę kalorymetrii
zużycia tlenu, porównując wartości zmiennych wyjściowych z modelu z wartościami rzeczywistymi,
poprzez określenie wskaźnika jakości dopasowania. Przyjęto, że wskaźnikiem pozwalającym ocenić czy
uzyskane zmienne wyjściowe z modelu są zgodne z ogólną wiedzą i doświadczeniem jest współczynnik
korelacji r. W pracy wykorzystano wyniki badań taśmy przenośnikowej chloroprenowej oznaczonej
symbolem 69/97.
W oparciu o wyznaczoną w kalorymetrze stożkowych dla natężenia promieniowania 50kWm-2
i 75kWm-2 wartość szybkości wydzielania ciepła QHRR oraz obliczoną wartość powierzchni pożaru Ap
i sprawności procesu palenia χ, przeprowadzono obliczenia (wzór 9) mające na celu wyznaczenie wartości
temperatury mieszaniny powietrza i gazów pożarowych Ta. Wyznaczone na podstawie modelu zmiany
temperatur oraz wartości rzeczywiste zmierzone w sztolni pożarowej, przedstawiono na rys. 4-2. Ponadto na
rys. 4-4, 4-5 i 4-6 przedstawiono obliczone, prognozowane wartości zmian stężenia tlenu XO2 w wyrobisku
chodnikowym (wzór 14) oraz emisji dwutlenku węgla XCO2 (wzór 19) i tlenku węgla XCO (wzór 16).
Wykorzystując analizę regresji prostej wykazano istnienie korelacji pomiędzy wartością temperatur wyznaczonych z modelu matematycznego dla natężenia promieniowania 50kWm-2 i 75kWm-2,
względem temperatury rzeczywistej zmierzonej w sztolni pożarowej. Najlepszą korelację dla wartości
temperatur obliczonych z modelu matematycznego opisanego zależnościami (8) oraz (9), wynoszącą
r = 0,9, uzyskano w oparciu o model liniowy, co dowodzi istnienia bardzo silnej zależności liniowej
między badanymi zmiennymi.
Podobnie jak w powyższy przypadku analizę regresji prostej zastosowano w celu wykazania istnienia
korelacji dla wartości udziału molowego O2, CO i CO2 obliczonych z modelu matematycznego. W przypadku udziału molowego tlenu O2, obliczonej z modelu matematycznego (wzór 14), najlepszą korelację,
r = 0,98, uzyskano w oparciu o model liniowy, co dowodzi istnienia bardzo silnej zależności liniowej
między badanymi zmiennymi (rys. 5-2.1.). Natomiast w przypadku udziału molowego tlenku węgla CO
wyznaczonego z modelu matematycznego (wzór 16) o istnieniu bardzo silnej zależności między badanymi
zmiennymi świadczy uzyskany współczynnik korelacji r = 0,92, a w przypadku molowego dwutlenku węgla
CO2 wyznaczonego z modelu matematycznego (wzór 19) współczynnik korelacji wyniósł r = 0,90.
Reasumując należy stwierdzić, że na podstawie szczegółowej analizy zjawisk pożaru taśmy przenośnikowej opracowany został model matematyczny pożaru taśmy. Wykazano istnienie znaczących
współzależności pomiędzy wynikami uzyskanymi na podstawie modelu matematycznego, a wynikami
otrzymanymi w drodze eksperymentów pożarowych dla układu rzeczywistego. Wyznaczone na podstawie modeli matematycznych wartości zmiennych wyjściowych pozwalają na prostą i łatwą interpretację
zachodzących podczas pożaru zjawisk i mogą być pomocne do analizy zagrożeń pożarowych związanych
ze stosowaniem taśm przenośnikowych w kopalniach.
Słowa kluczowe: model matematyczny, pożary podziemne, palność materiałów, taśma przenośnikowa
1. Introduction
The mines are particular locations in respect of fire hazard. Hard working conditions
and limited escape way cause that even the smallest fire can lead to severe consequences,
such as victims and considerable material losses. Exogenous fires are particularly serious
danger to miners working underground. In the course of them, subject to burning may
be all flammable materials present in the mine, being elements of mining machinery
or equipment, or used in various technical solutions associated with production of coal
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(conveyor belts, electrical cables, hydraulic conduits, elastic air ducts, filling fabric,
mineral oils, plastics pipes organic binders, etc.).
The largest group of products made of organic materials and used in mine underground workings are conveyor belts. In spite of rigorous enforcement of provisions
included in the standards relating to fire-resistance characteristics of belts, and strict
safety measures, still there is a fire hazard connected, for instance, with susceptibility to
spontaneous heating of abrasion products of rubber cover of conveyor belts, officially
qualified as fire-resistant and fulfilling the criteria of fire-resistance being in force in
mining industry (Wachowicz, 2004).
The scientific aspects of conducting fire-fighting actions in hard coal mines,
elaborated by W. Budryk (1954) are of vital importance in mining theory and practice.
These rules have been generally recognized, and are realized by many scientists coming
from the so-called “Polish school in aerology”. Here, there must be quoted the works
considered fundamental, that is those of H. Czeczott (1927, 1928), W. Budryk (1950),
W. Trutwin (1971, 1972), raising the subject matter of air flow process, transient states
in mine ventilation networks, and analytical methods to solve them. The mathematical
aspects of modeling transient states in air flow in a mine ventilation network, including
the processes of exchange of energy, mass and momentum are discussed in the works of
J. Litwiniszyn (1954, 1957). Of importance are also the achievements of such Polish scientists as H. Bystroń (1971), Z. Maciejasz and J. Roszkowski (1966), as well as A. Frycz
(1969), being the works considerably influencing the development of mining aerology.
2. Mathematical model of conveyor belt fire in mine gallery
The exogenous fire is characterized by complexity and interrelation of defined
physical parameters which determine directly the phenomenon of fire. Underground fires
are principal factors generating disturbances in the process of flow of air and fire-gas
mixture along the gallery (Dziurzyński and Krawczyk, 2001; Dziurzyński and Pałka,
2001). On the basis of results of tests conducted with the use of cone calorimeter method
and fire-test gallery, there have been formulated some mathematical models that make it
possible to analyze the phenomenon of exogenous fire in the presence of organic material. A trial to formulate a mathematical model of the fire spot, is chiefly aimed at linking
selected physical parameters in such a way so as to they could be verified and included
in a program enabling to analyze the effect of fire on the atmosphere of the gallery and
resulting potential hazards. On the other hand, the results obtained in experiments will
be utilized in verification of the mathematical model that determines the phenomenon of
conveyor belt fire. In the mathematical formulation of the combustion process, important
proves to be the assumption of proportionality of one selected parameter determining
the process of combustion in relation to the other (Dziurzyński, 1998, 2001; Edwards
and Hwang, 1999; Campos et al., 2004; Skotniczy, 2008).
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2.1. Parameters characterizing dynamics of process of conveyor
belt combustion in fire spot
The dynamics of fire of organic material, in this case conveyor belt, can be described
by parameters determining directly the occurring processes, which will be presented
below in his charter. (Drysdale, 1998; Dziurzyński, 1998, 2001; Smith and Greek,
1987).
2.1.1. Heat load of fire
The destructive potential of fire depends chiefly on the amount of organic material
(fuels, flammable material) collected in the area covered by the fire. A measure of the fire
burden of materials collected in a mine gallery is heat potential defined by relationship:
n
Qv (mi Csi )
(1)
i 1
where:
Qv
mi
Csi
— amount of heat released from fire, J
— i-th mass of organic material collected, kg
— heat of combustion of i-th type organic material, J kg-1.
2.1.2. Areas of conveyor belt covered by fire Ap and Ac of
heat exchange obtained from cone calorimeter
and fire-test gallery
The fire-covered area Ap is a parameter which, within duration of the fire, undergoes sudden changing in a time unit. In the case of organic materials, the process of
combustion proceeds mainly on its surface, and not inside, which occurs is the case of
coal (coal porosity), which considerably lowers the effective fire area, and is given by
the following relationships (Carvel et al., 2001; Oka and Kurioka, 2006)):
Ap Qv
sz
Q THE
(2)
where:
Ap — fire-covered area, m2
QTHE — amount of heat released from cone calorimeter, J m-2
Qvsz — amount of heat released in fire- test gallery, J.
The fire-covered surface of the conveyor belt assumes the proportionality of the
mass loss rate dMp /dt to unit fire rate kc, j. The rate of mass loss dMp /dt of the burning
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conveyor belt per unit time, for the data obtained from the cone calorimeter and from
fire-test gallery may be expressed by equation (Dziurzyński, 1998; Lowndes et al., 2007;
Oka and Kurioka , 2006):
dM p
dt
Ap HRR
kc , j
(3)
where:
dMp/dt
kc, j
Ap
QHRR
—
—
—
—
mass loss rate, kg s-1
unit mass loss rate taken from cone calorimeter, kg m-2 s-1
fire-covered area, m2
rate of heat released from cone calorimeter, W m-2
On the other hand, the mass loss of Mp of the burning conveyor belt, for the data
obtained from cone calorimeter and fire-test gallery may be expressed by relationship:
Mp Ap QTHE
Cs
(4)
where:
Ap — fire-covered area, m2
QTHE — amount of heat released taken from cone calorimeter, J m-2
Cs — heat of combustion taken from cone calorimeter, J kg-1
The area of heat exchange Ac is a parameter that enables to define the area of
heat exchange in the range covered by the process of combustion of the conveyor
belt, informally called the area seen from the fire spot, and described by relationship (Dziurzyński, 1998; Lowndes et al., 2007; Oka and Kurioka , 2006):
Ac Q v sz
QHRR
(5)
where:
Ac — heat-exchange area, m2
•
Qvsz — amount of heat released from fire spot, J s-1
QHRR — average heat released rate , W m-2.
2.1.3. Length of section of burnt conveyor belt
On the basis of a total amount of heat released, determined using the cone calorimeter, QTHE
(total heat evolved), and the computed amount of heat released in a given time unit in
•
the fire-test gallery, Qvsz, it is possible to determine the length of the section of burnt
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belts. The length determined of the belt burnt in a given time unit may be expressed by
relationship:
L t where:
LΔt
Qvsz
QTHE
d
—
—
—
—
Qvsz
QTHE d
(6)
length of burnt belt section per unit time, m
amount of heat released from fire in the fire-test gallery, J
amount of heat released, determined using cone calorimeter, J m-2
width of conveyor belt, m.
2.1.4. Temperature of mixture of air and fire gases leaving
conveyor belt fire spot for data obtained from fire-test
gallery
The temperature of the layer of air and fire gas mixture Ta flowing around the fire
spot can be determined on the basis of energy balance in the gallery seized by the fire.
During an exogenous fire, the chemical reactions proceed, as a result of which the released
heat, delivered to the system in an isobaric process equals to the change of its enthalpy
(Janoszek, 2009; Wachowicz and Wypior, 2003). Because of the lack of capability to
measure the quantity of loss, by means of available measuring methods, in the fire-test
gallery, and due to the fact that during the underground fire the combustion is never
ideal, and the temperature is lower than the theoretical value, the heat emitted into the
gallery has been reduced by the coefficient of proportionality χ, where the parameter χ
represents the effectiveness of combustion, and is a ratio of the net quantity of emitted
heat to the product of mass loss rate and heat of combustion of the tested conveyor belt
sample resulting from measurement in the cone calorimeter (Babrauskas, 1992).
On an assumption of the lack of heat exchange through the walls of the gallery
(adiabatic process) and of energy loss on local resistances, and with p = const., the
energy balance for such a system has the form (Poniewierski et al., 2003; Schabacker
and Bettelini, 2001):
Q vsz Ho Ha
(7)
where:
•
Qvsz — amount of heat released from the fire, J s-1
•
Ho — stream of energy of the agent (air) at the inlet, J s-1
•
Ha — stream of energy of the agent (air) at the outlet, J s-1.
After proper transformations have been made, the above equation of energy balance
may be presented in the form:
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Qvsz To o Ao Cpoo Ta o Ao Cpoo
(8)
where:
•
Qvsz
To
Ta
Ao
Cpo
vo
ρo
—
—
—
—
—
—
—
quantity of heat released from fire, J s-1
temperature of air at inlet to gallery, K
temperature of air and fire gases leaving fire zone, K
cross-section area of working, m2
specific heat of air, J kg-1K-1
air flow rate at inlet to working, K
local density of fluid, kg m-3.
Taking this, it is possible to obtain the equation that enables to find an average temperature of air flowing around the fire spot (Edwards and Hwang, 1999; Poniewierski
et al., 2003):
Ta To where:
QHRR
Ap
Mp
Cs
—
—
—
—
Qvsz
o Ao Cpo o
To Ap QHRR
Mp Cs
To o Ao Cpoo
o Ao Cpoo
(9)
amount of heat released, determined using cone calorimeter, W m-2
area covered by combustion (fire area), m2
mass loss of fuel in fire, kg
heat of combustion determined using cone calorimeter, J kg-1.
The temperature of fire gases Tf emitted from the fire into the roof part of the gallery within a given unit of time, depending on the height of gallery, can de determined
on the basis of equation proposed in the work (Kouchinsky, 2007), namely:
1/ 3
To
2/ 3
5 / 3
Tf 9.1 (0.7 A p QHRR ) (z zo ) To
2 2
g
cos
C
po o where:
QHRR
z
zo
g
cosα
Tf
ρo
—
—
—
—
—
—
—
amount of heat released, determined using cone calorimeter, W m-2
height of gallery, m
theoretical height of fire spot, m
acceleration of gravity, m s-2
slope angle of gallery
temperature of fire gases, K
local density of fluid, kgm-3, kg m-3.
(10)
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The parameter zo called the theoretical (hypothetical) height of the fire spot may be
determined on the basis of relationship proposed in the work (Merci and Vandenvelde,
2007), and formulated as:
z o 0 , 083 5 Qvsz
2
2 , 04
Ap
2
(11)
where:
•
Qvsz — quantity of heat released from fire spot, J s-1
Ap — area of fire, m2.
2.1.5. Dynamics of process of conveyor belt combustion
in fire spot
The dynamics of the conveyor belt combustion process can be expressed by an
•
assumption of proportionality of the amount of heat Qvsz emitted from the fire spot in
relation to fire-covered area Ap, heat of combustion Cs and unit rate of mass loss kc, j of
the conveyor belt, and given by relationship (Mowrer, 2003):
where:
Cs
QHRR
Ap
χ
—
—
—
—
Ap QHRR
dM p
Cs
dt
(12)
heat of combustion determined using cone calorimeter , J kg-1
average rate of heat released determined using cone calorimeter, W m-2
surface seized by combustion ( fire-covered area), m2
coefficient characterizing the dynamics of combustion process.
2.2. Variation of oxygen concentration and emission of toxic
components of fire gases
2.2.1. Model of variation of oxygen concentration
in a gallery
In 1917, W. Thorton presented that the amount of heat released from the fire spot in
the course of total combustion of most liquid and gaseous organic substances depends on
the volume of oxygen consumed in the combustion process. The Thorton’s rule makes
it possible to conclude that in order to determine the amount of heat released during the
combustion, it is sufficient a total mass loss of oxygen in the reaction of thermo-oxidation. Hence, with the aim to determine a total amount of heat released in the course of
516
combustion, the relationship is used (Thornton, 1917; Babrauskas, 1984; Hugget, 1980;
Opstad, 1991; Wachowicz, 2001):
Q vsz ( X OO2 Vo X SO2 VS ) O2 E
where:
•
Qvsz
XOO2
XSO2
Vo
VS
E
ρO2
(13)
amount of heat released from fire, MJ s-1
real concentration of oxygen in air at inlet to gallery (molar portion),
real concentration of oxygen in air at outlet from gallery (molar portion),
stream of air volume delivered to gallery, m3s-1
stream of fire gas volume, m3s-1
heat released during combustion per unit oxygen consumption,
(E = 13,1 MJ kg-1)
— density of oxygen in normal conditions, kg m-3.
—
—
—
—
—
—
By making use of relationship (13), one can evaluate the dynamics of variation of
oxygen concentration in the gallery, in the conditions of occurred fire of organic material
through formulating the following equation:
X SO2 where:
QHRR
X OO2
Ap
S
X O2
Vo
VS
E
ρO2
X OO2 Vo O2 E Q vsz
VS O2 E
X OO2 Vo O2 E Ap QHRR
VS O2 E
(14)
average rate of heat released determined using cone calorimeter, MWm-2
real concentration of oxygen at inlet to gallery (molar portion),
fire-covered area, m2
real concentration of oxygen at outlet from gallery (molar portion),
stream of air volume flowing into gallery, m3s-1
stream of volume of fire gases leaving gallery, m3s-1
heat emitted during combustion per unit oxygen consumption,
(E = 13,1 MJ kg-1)
— density of oxygen in normal conditions, kg m-3.
—
—
—
—
—
—
—
2.2.2. Emission of carbon monoxide in the conditions
of conveyor belt fire
In the case when the process of combustion of organic material proceeds with deficiency of air (incomplete combustion), the fire gases being a product of this incomplete
combustion will contain flammable components in the form of carbon monoxide CO.
The amount of heat obtained in this case will be smaller than in the case of total com-
517
bustion (Drysdale, 1998). The ratio of oxygen consumed in the combustion process for
production of CO to total amount of consumed oxygen is defined by a variable fCO. This
parameter may be determined on the basis of the following correlation (Lougheed and
Hadjisophocleous, 2001; Wachowicz, 2000):
1
15
Q vsz
fco 0,0049 0,1579 5
o To Cpo gAo where:
•
Qvsz
ρo
To
Cpo
g
Ao
—
—
—
—
—
—
(15)
amount of heat released from fire in fire-test gallery, J s-1
density of air, kg m-3
temperature of air at inlet to gallery, K
specific heat of air, Jkg-1K-1
acceleration of gravity, ms-2
hydraulic diameter of working, m2.
The mass portion of CO in fire gases leaving the fire spot can be presented by empirical equation (Mowrer, 2003):
S
fCO
X CO
dMp
dt
mo mf
Ap QHRR
f CO
kc , j
(16)
mo m f
where:
QHRR — average rate of heat released determined using cone calorimeter, MWm-2
Ap — fire-covered area, m2
fCO — parameter defining ratio of oxygen consumed in the combustion process
for production of CO to total amount of oxygen consumed,
•
mo — stream of air mass at inlet to gallery, kg s-1
•
mf — stream of mass of fire gasses emitted from fire source into flowing air, kg s-1
dMp /dt — mass loss rate,, kg s-1
kc, j — unit rate of mass loss, kg m-2 s-1.
2.2.3. Emission of carbon dioxide in the gallery
in the conditions of conveyor belt fire
In the case when the process of combustion of organic material proceeds in the atmosphere of sufficient volume o fair, then all the flammable components of the organic
material, that is hydrogen H and sulphur S become oxidized to carbon dioxide CO2,
water H2O and sulphur dioxide SO2 (Drysdale, 1998).
518
The mass portion of carbon dioxide CO2 in the fire gases may be assessed in accordance with the empirical formula (Lougheed & Hadjisophocleous, 2001; Mowrer, 2003):
S
X CO
f CO 2
2
Ap QHRR
dMp
dt
f CO2
mo mf
k c, j
mo m f
(17)
where:
fCO2 — parameter defining ratio of oxygen consumed during combustion process
for production of CO2 to total volume of oxygen consumed,
dMp /dt — rate of mass loss of flammable material, kg s-1
•
mo — stream of air mass at inlet to gallery, kg s-1
•
mf — stream of mass of fire gases emitted from fire source to flowing air, kg s-1.
The stream of mass of fire gasses (fume) leasing the fire-covered zone may be evaluated on the basis of the following relationship (Guillermo et al., 2004):
1/ 3
0,6 g cos 1/ 3
5/ 3
m f 0,21o (Ap QHRR ) (z zo )
Cpo o To where:
QHRR
ρo
Cpo
To
g
cosα
z
Ap
—
—
—
—
—
—
—
—
(18)
average rate of heat released determined using cone calorimeter, MWm-2
density of air at inlet to gallery, kg m-3
specific heat of air, MJ kg-1 K-1
temperature of air, K
acceleration of gravity, m s-2
slope of gallery, °
coordinate along height of gallery, m
fire-covered area, m2.
By using relationship (17), the equation above may be brought to the form (Kunikane et al., 2006):
A p QHRR
S
fCO2
X CO
2
kc, j
1/ 3
0,6 g cos 1/ 3
5 / 3
m o 0,21o (Ap QHRR ) ( z zo ) Cpo o To where:
Cs — heat of combustion taken from cone calorimeter, MJ kg-1
(19)
519
The parameter that defines the ratio of oxygen consumed in the combustion process
for production of CO2 to a total volume of oxygen consumed may be evaluated on the
basis of relationship (Mowrer, 2003; Wachowicz, 2000):
Q vsz
f CO2 0 , 0282 1,3632 o Cpo To AVo
0 , 05
(20)
3. Description of test stands and methodology of
experimental investigations
3.1. Test stands-description and structure
Experimental investigations of fire dynamics have been realized on the basis of a cone
calorimeter and the fire-test gallery being available at the Central Mining Institute. Testing
the conveyor belts in the fire-test gallery makes it possible to determine the capability of
self-extinguishing of the belt outside the fire spot, where the source of fire is a 300 kg
mass of dry pinewood. The criterion of the test is a defined length of the burnt out belt
section (40 m). In turn, when testing conveyor belt with the use of oxygen consumption
calorimetry, there are determined the parameters that define the tested organic material
and enable to construct the models describing the intensity of fire dynamics.
3.2. Methodology
3.2.1. Determining fire-resistance characteristics of
conveyor belts with the use of cone calorimeter
The method of testing the flammability using the cone calorimeter relies on burning a sample of material in consequence of an effect of thermal radiation generated by
a conical heat emitter and on measuring the concentration of oxygen in the combustion
gases. The recorded results of oxygen concentration changes X SO2 enable to determine
the intensity of heat emission in the course of burning of the tested organic matter (Hugget, 1980; Sobieszczuk i Wachowicz 1998; Wachowicz, 2000, 2001).
The schematic diagram of the stand for testing the intensity of heat emission and for
analyzing the composition of gases resulting from thermo-oxidation reactions by means
of the cone calorimeter, in accordance with ISO 5660-1 method, have been presented
in Fig. 1.
520
Laser system to mensuration of temperature
Sensor of temperature and difference pressure
Exhaust
Fan
Cone heater
Filter of reservoir of soot
Spark fuse
Valve
Sensor
of flow
Sample
Load cell
Fig. 1. Schematic diagram of stand to investigate intensity of heat emission
by means of cone calorimeter in accordance with ISO 5660–1 method
Conveyor belt
Wood
m
42
m
100
Place of recruitment
of the fire-gases
Air fan
Sample of conveyor belt
Air 1.2 m/s
3m
2m
4m
Fig. 2. Schematic diagram of installation for testing flammability of conveyor
belts using fire-test gallery (Wachowicz, 2001)
521
3.2.2. Determining fire-resistance characteristics of
conveyor belt samples by means of fire-test gallery
The fire-test gallery method makes it possible to assess whether the tested conveyor
belt which, in consequence of an effect of external fire source, reveals the fire-resistance
properties, or creates a potential hazard of spreading the fire (Wachowicz, 2000, 2001).
On the basis of this method, the samples of the tested conveyor belt are subjected to
effects of heat from the flame of wood burning in the fire-test gallery, and then there is
measured the length of non-burnt belt sections, which has been schematically presented
in Fig. 2. In the course of fire, there is measured the temperature of interior of the gallery
by means of thermocouples positioned in five points of the fire-test gallery, and spaced
by 10 m. The thermocouples are located in the central point of the gallery, at a height
of 1 m from the floor. Measured are also the concentrations of fire gases at a distance
of 10 m from the end of gallery (CO, CO2 and O2). After the fire has gone out, there is
measured the length of non-burnt section of the belt on which no signs of damage due
to direct effect of flame have been found.
4. Results of experimental investigations and their
comparison with results of modeling computations
Presented below are the results of investigations of selected samples of chloroprene
conveyor belt, marked with a symbol 69/97, and obtained in the course of testing the
flammability with the use of cone calorimeter and fire-test gallery, taking into account
more important parameters when constructing mathematical models. Shown in Fig. 3
is the rate of heat emission in the course of burning the belt in the fire-test gallery, with
60 minute test duration.
In turn, Table 1 presents the results of more important parameters used in the mathematical model that characterizes the flammability of the conveyor belt marked with
69/97 symbol.
TABLE 1
Results of flammability tests using cone calorimeter method for sample 69/97
-2
-2
– radiation intensity of 50kW m and 75 kW m
Average value of 3 measurements
69/97-TTG-3P-1000
50 kW/m2
75 kW/m2
Measuring parametr
Ignitron time – ti
Total heat emitted – QTHE
Unit rate of mass loss – kc, j
Average effective heat of combustion – Cs
Heat emission rate – QHRR
[s]
[MJ m-2]
[g m-2 s-1]
[MJ kg-1]
[kW m-2]
51,14
131,51
5,01
13,89
105,19
17,89
219,55
5,49
17,89
163,62
522
Heat released, Qvsz [MW]
3,5
3,12
3,17
3
2,5
1,92
2
1,5
1
0,67
0,67
0,31
0,5
0,3
0,27
0
0
400
800
1200
1600
2000
2400
2800
3200
3600
4000
Time, t [s]
Fig. 3. Diagram of determining net heat emitted in fire-test gallery when testing
a conveyor belt marked with 69/97 symbol (Wachowicz, 2001)
On the basis of the rate of emitted heat QHRR determined in a cone calorimeter for
heat stream densities of 50 kWm-2 and 75 kWm-2 , and of calculated value of fire-covered
area Ap and efficiency of combustion process χ, the computations have been made- relationship (9) – aimed at determining the value of temperature of the mixture of air and
fire gases Ta in a given moment of fire duration. The temperature changes determined
on the basis of the model, and real values measured in the fire-test gallery, Ta = Ta(t), for
the tested conveyor belt, marked 69/97, are presented in Fig. 4.
In turn, Fig. 5 presents the predicted values of change of temperature, computed
for sample 69/97, Tf of fire gases leaving the fire zone at the height z = 1 m (similarly as
Temperature Ta, [K]
500
450
400
350
300
250
0
600
1200
1800
2400
3000
3600
4200
Time, [s]
Change of temperature for 50 kW/m2 – mathematical model (9)
Change of temperature for 75 kW/m2 – mathematical model (9)
Change of temperature measured in fire-test gallery – thermocouple 24 m
Fig. 4. Change of temperture o fair-gas mixture Ta determined on the basis of values measured
in fire-test gallery and computed from model (9) – sample 69/97
523
in fire-test gallery), taking advantage of: measured net quantity of heat released in the
•
fire-test gallery, Qvsz, computed value of fire-covered area Ap, and value of heat released
QHRR taken from cone calorimeter.
In addition, Figs. 6, 7 and 8 present the computed, for the tested sample marked
69/97, predicted values of variation of oxygen concentration XO2 in the gallery (14),
950
850
Tf, [K]
750
650
550
450
350
250
0
600
1200
1800
2400
3000
3600
t, [s]
Change of temperature of fire gases – thermocouple 24 m
Change of temperature of fire gases for 50 kW/m2 – mathematical model (9)
Change of temperature of fire gases for 75 kW/m2 – mathematical model (9)
Fig. 5. Change of temperature Tf of fire gases at the height in gallery z = 1 m ,for values obtained
in fire-test gallery and obtained from model – sample 69/97
0,22
0,21
XO2
0,2
0,19
0,18
0,17
0,16
0,15
0
600
1200
1800
2400
3000
3600
t, [s]
Change of concentrating of oxygen – measured in fire-test gallery
Change of concentrating of oxygen for 50 kW/m 2 – mathematical model (14)
Change of concentrating of oxygen for 75 kW/m 2 – mathematical model (14)
Fig. 6. Variation of oxygen O2 concentration in layer of fire gases at height in gallery z = 1 m
for values obtained in fire-test gallery and computed from model – sample 69/97
524
0,1
XCO2
0,08
0,06
0,04
0,02
0
0
600
1200
1800
2400
3000
3600
t, [s]
Changes of carbon dioxide concentration – measured in fire-test gallery
Changes of carbon dioxide concentration for 50 kW/m2 – mathematical model (19)
Changes of carbon dioxide concentration for 75 kW/m2 – mathematical model (19)
Fig. 7. Variation CO2 concentration in layer of fire gases at height in gallery z = 1 m for values
obtained in fire-test gallery and computed from model (19) – sample 69/97
0,01
0,008
XCO
0,006
0,004
0,002
0
0
600
1200
1800
2400
3000
3600
t, [s]
Changes of carbon monoxide concentration – measured in fire-test gallery
Changes of carbon monoxide concentration for 50 kW/m 2 – mathematical model (16)
Changes of carbon monoxide concentration for 75 kW/m 2 – mathematical model (16)
Fig. 8. Variation of CO concentration in layer of fire gases at height in gallery z = 1 m for values
obtained in fire-test gallery and calculated from model (16) – sample 69/97
and of emission of carbon dioxide XCO2 (19) and carbon monoxide XCO (16) to flowing
stream of autonomous air, by using to this end the net quantity of heat Qvsz released in the
fire-test gallery, and heat released rate QHRR determined by means of cone calorimeter,
as well as computed value of belt area Ap seized by combustion.
525
5. Analyses of measurement results
As a criterion of accuracy of mathematical models applied in analyzing the dynamics of the fire, there has been assumed to demonstrate the existence of linear regression
model among the values of parameters obtained during the experiment in the fire-test
gallery in relation to parameters obtained on the basis of the mathematical model. The
measure of reliability of obtained results in the form of a regression equation is the
coefficient of correlation r.
5.1. Demonstration of existence of correlation among
the results of temperature of fire gases obtained
experimentally and based on mathematical model
From relationships (9) and (10), and from fire-test experiments conducted, the values
of temperatures have been found for air and fire gases in the fire zone. By using the linear
regression analysis, a trial has been made to demonstrate the existence of correlation
between the values of temperatures found from the mathematical model, presented by
relationship (9) in a specified duration of the experiment, being in the range 0÷3600 s,
for heat stream density being 50kWm-2 and 75kWm-2 , in relation to real temperature
measured in the fire-test gallery.
Subsequently, a trial has been made to demonstrate the existence of correlation
for temperature values of fire gases found from the mathematical model presented by
relationships (10) in a specified duration of the experiment, being in the range 0÷3600 s,
and for heat stream density being 50kWm-2 and 75kWm-2, in relation to real temperature
measured in the fire-test gallery.
The best correlation for temperature values computed from the mathematical model,
described by relationships (8) and (9), being r = 0,9, has been obtained on the basis of
a linear model, which justifies the existence of very strong linear relationship between
the analyzed variables [26].
5.2. Demonstration of existence of correlation between
results of molar portions of O2, CO and CO2 in fire gases
obtained from experimental layout and based
on mathematical model
The lineal regression analysis, similarly as in the case discussed in 5.1 above, has
been applied with the aim to demonstrate the existence of correlation for the values of
molar portions of O2, CO and CO2 computed from the mathematical model, described
by relationships (14), (16) and (19), respectively, based on an average rate of heat emission determined by means of the cone calorimeter, for heat stream densities 50 kWm-2
526
and 75kWm-2, and real concentrations of gases measured in the fire-test gallery, within
the time range 0÷3600 s.
The best correlation r = 0,98 (r 2 = 96), for the values of molar portion of oxygen O2,
computed from mathematical model (14), has been obtained based on a linear model,
which justifies the existence of a very strong linear relationship between the analyzed
variables (Fig. 9).
0,215
0,210
0,205
0,200
0,195
0,190
0,185
XO2(50 kW/m2; t = 0÷3600; 1 m):
r 2 = 0,9635; r = 0,9816;
y = –0,004 + 1,0057x
0,180
0,175
XO2(75 kW/m2; t = 0÷3600; 1 m):
r 2 = 0,9704; r = 0,9851;
y = 0,0032 + 0,9717x
0,170
0,165
0,160
0,16
0,17
0,18
0,19
0,20
0,21
0,22
0,23
X O2 sz
Fig. 9. Dependence of change of oxygen concentration XO2 (50 kW/m2; t = 0÷3600; 1 m)
and XO2(75 kW/m2; t = 0÷3600; 1 m) determined from mathematical model (14)
in relation to change of oxygen concentration XO2sz from measurement
in fire-test gallery – sample 69/97
The best correlation for the values of molar portion of CO determined from the
mathematical model described by relationship (16), has been obtained based on a linear
model, being in the range of r = 0,93 (r 2 = 0,86), thereby proving the existence of a very
strong linear relationship between analyzed variables (Fig. 10).
In the case of molar portion of CO2 determined from the mathematical model described by relationship (19), the best correlation has also been obtained based on a linear
model. The coefficient of correlation was r = 0,88 (r 2 = 0,78), which justifies the existence
of substantial lineal relationship between analyzed variables (Fig. 11).
6. Sumary of investigation results
To evaluate the developed mathematical model, a specially designed experiment
has been used. In the presented case, these are the data obtained, and the method of
oxygen consumption calorimetry. One of the method used to evaluate the reliability of
527
0,008
0,007
0,006
0,005
0,004
XCO(50 kW/m2; t = 0÷3600; 1 m):
r 2 = 0,8569; r = 0,9257;
y = –0,0006 + 0,759x
XCO(75 kW/m2; t = 0÷3600; 1 m):
r 2 = 0,8562; r = 0,9253;
y = –0,0005 + 0,5954x
0,003
0,002
0,001
0,000
-0,001
-0,001
0,000
0,001
0,002
0,003
0,004
0,005
0,006
0,007
0,008
0,009
X CO sz
Fig. 10. Dependence of change of oxygen concentration XCO (50 kW/m2; t= 0÷3600; 1 m)
and XCO (75 kW/m2; t = 0÷3600; 1 m) determined from mathematical model (16)
in relation to change of oxygen concentration XCOsz from measurement
in fire-test gallery – sample 69/97
0,045
0,040
0,035
0,030
0,025
XCO2(50 kW/m2; t = 0÷3600; 1 m):
r 2 = 0,7785; r = 0,8823;
y = –0,0012 + 0,3656x
XCO2(75 kW/m2; t = 0÷3600; 1 m):
r 2 = 0,7754; r = 0,8806;
y = –0,001 + 0,3007x
0,020
0,015
0,010
0,005
0,000
-0,005
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0,09
0,10
X CO2 sz
Fig. 11. Dependence of change of oxygen concentration XCO2 (50 kW/m2; t = 0÷3600; 1 m)
and XCO2 (75 kW/m2; t = 0÷3600; 1 m) determined from mathematical model (19)
in relation to change of oxygen concentration XCO2sz from measurement
in fire gallery – sample 69/97
the designed model is to compare the values of model input variables with real values,
based on defining the index of quality of fitting, and carrying out tests in relation to assumptions of the model. An example of such an index is the correlation coefficient r,
making possible to evaluate whether the output data obtained agree with the general
knowledge and experience.
528
An analysis of experimental data and of output variables from the mathematical
and numerical models, enable to make the following observations:
1. The discussions presented made it possible to demonstrate that among the empirical parameters that determine the flammability of conveyor belts, such as:
• total heat released, THR,
• heat released rate, HRR,
• heat of combustion, HOC,
• unit rate of mass loss, kc, j,
determined with the use of cone calorimeter, and the net amount of heat emitted,
determined based on the results of experiments in the fire-test gallery, there are
relationships enabling to determine:
• fire-covered area, Ap,
• visible area of fire, Ac,
• rate of mass loss of conveyor belt, dMp/dt,
• changes of length of burnt belt section in specified time unit, L∆t,
• average value of temperature of mixture of air and fire gases flowing around
fire spot, Ta,
• changes of oxygen concentration and emission of fire gases in area seized by
exogenous fire, X SO2, X SCO2, X SCO,
• temperature of layer of fire gases Tf emitted from fire spot into roof part of
gallery in specified time unit.
2. The existence of substantial correlation has been found between output variables
obtained for the mentioned above mathematical models, and the parameters
measured in the fire-test gallery (Janoszek, 2009). The best correlations were
obtained on the basis of linear model, respectively:
• for results of temperature of fire gases, obtained experimentally and based
mathematical model, the existence of substantial interrelation has been found
between individual output variables, at average level r = 0,9,
• for results of molar portion of oxygen O2 in fire gases obtained from experimental setup, and based on mathematical model, the existence of substantial
interrelation has been found between individual output variables, at average
level r = 0,95,
• for results of molar portion of carbon dioxide CO2 in fire gases obtained from
experimental setup, and based on mathematical model, the existence of very
strong and substantial interrelation has been found between individual output
variables, at average level r = 0,90,
• for results of molar portion of carbon monoxides CO in fire gases obtained
from experimental setup, and based on mathematical model, the existence of
very strong interrelation has been found between output variables, at average
level r = 0,92.
529
7. Conclusions
1. On the basis of a detailed analysis of phenomena of the conveyor belt fire,
a mathematical model of belt fire has been developed.
2. Demonstration of substantial interrelations between results obtained on the basis
of the mathematical model, and the results obtained through fire experiments for
a real system, confirm the accuracy of developed mathematical models.
3. Parameters determined with the use of cone calorimeter, such as average effective heat of combustion Cs, unit mass loss rate kc,j, rate of heat released QHRR
and amount of released heat QTHE, provided the possibility to predict the size of
conveyor belt fire in a gallery.
4. Values of output data determined on the basis of mathematical model, enable to
perform simple and direct interpretation of phenomena occurring in the course
of fire, and may be helpful in making analyses of fire hazards related to using
conveyor belts in the mines.
5. Method presented may be utilized in evaluating the hazards related to using
conveyor belts through predicting the main parameters which determine the
dynamics of fire.
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Received: 17 March 2009